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人気のある代数 >

solvefor a,3a^2+3a+at=(30)/t

解

解く

a, 3 a^{2} + 3 a + a t = \frac{30}{t}

解

a = \frac{- 3 t - t ^{2} + ( 3 t + t ^{2} ) ^{2} + 360 t}{6 t}, a = \frac{- 3 t - t ^{2} - ( 3 t + t ^{2} ) ^{2} + 360 t}{6 t}; t \neq = 0

解答ステップ

3 a^{2} + 3 a + a t = \frac{30}{t}

以下で両辺を乗じる:

t

3 a^{2} t + 3 a t + a t^{2} = 30; t \neq = 0

30

を左側に移動します

3 a^{2} t + 3 a t + a t^{2} - 30 = 0; t \neq = 0

標準的な形式で書く

a x^{2} + b x + c = 0

3 t a^{2} + (3 t + t^{2}) a - 30 = 0; t \neq = 0

解くとthe二次式

a_{1, 2} = \frac{- ( 3 t + t ^{2} ) \pm ( 3 t + t ^{2} ) ^{2} - 4 \cdot 3 t ( - 30 )}{2 \cdot 3 t}

簡素化

(3 t + t^{2})^{2} - 4 \cdot 3 t (- 30) : (3 t + t^{2})^{2} + 360 t

a_{1, 2} = \frac{- ( 3 t + t ^{2} ) \pm ( 3 t + t ^{2} ) ^{2} + 360 t}{2 \cdot 3 t}; t \neq = 0

解を分離する

a_{1} = \frac{- ( 3 t + t ^{2} ) + ( 3 t + t ^{2} ) ^{2} + 360 t}{2 \cdot 3 t}, a_{2} = \frac{- ( 3 t + t ^{2} ) - ( 3 t + t ^{2} ) ^{2} + 360 t}{2 \cdot 3 t}

a = \frac{- ( 3 t + t ^{2} ) + ( 3 t + t ^{2} ) ^{2} + 360 t}{2 \cdot 3 t} : \frac{- 3 t - t ^{2} + ( 3 t + t ^{2} ) ^{2} + 360 t}{6 t}

a = \frac{- ( 3 t + t ^{2} ) - ( 3 t + t ^{2} ) ^{2} + 360 t}{2 \cdot 3 t} : \frac{- 3 t - t ^{2} - ( 3 t + t ^{2} ) ^{2} + 360 t}{6 t}

二次equationの解:

a = \frac{- 3 t - t ^{2} + ( 3 t + t ^{2} ) ^{2} + 360 t}{6 t}, a = \frac{- 3 t - t ^{2} - ( 3 t + t ^{2} ) ^{2} + 360 t}{6 t}; t \neq = 0

グラフ

人気の例

7 A^{2} - 11 A - 6 = 0

3(2x+8)^2+18=45

3 (2 x + 8)^{2} + 18 = 45

x = 2 x^{2} - 1

x^2+2x+1=4x^2-12x+9

x^{2} + 2 x + 1 = 4 x^{2} - 12 x + 9

0 = 3 x^{2} - 48