12+7x-21=-8(3-x)4x

Solution for 12+7x-21=-8(3-x)4x equation:

12+7x-21=-8(3-x)4x

We move all terms to the left:

12+7x-21-(-8(3-x)4x)=0

We add all the numbers together, and all the variables

7x-(-8(-1x+3)4x)+12-21=0

We add all the numbers together, and all the variables

7x-(-8(-1x+3)4x)-9=0


We calculate terms in parentheses: -(-8(-1x+3)4x), so:

-8(-1x+3)4x

We multiply parentheses

32x^2-96x

Back to the equation:

-(32x^2-96x)


We get rid of parentheses

-32x^2+7x+96x-9=0

We add all the numbers together, and all the variables

-32x^2+103x-9=0

a = -32; b = 103; c = -9;
Δ = b2-4ac
Δ = 1032-4·(-32)·(-9)
Δ = 9457
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9457}=\sqrt{49*193}=\sqrt{49}*\sqrt{193}=7\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(103)-7\sqrt{193}}{2*-32}=\frac{-103-7\sqrt{193}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(103)+7\sqrt{193}}{2*-32}=\frac{-103+7\sqrt{193}}{-64}
$