2(7+5)=2x(4x-3)

Solution for 2(7+5)=2x(4x-3) equation:

2(7+5)=2x(4x-3)

We move all terms to the left:

2(7+5)-(2x(4x-3))=0

We add all the numbers together, and all the variables

-(2x(4x-3))+212=0


We calculate terms in parentheses: -(2x(4x-3)), so:

2x(4x-3)

We multiply parentheses

8x^2-6x

Back to the equation:

-(8x^2-6x)


We get rid of parentheses

-8x^2+6x+212=0

a = -8; b = 6; c = +212;
Δ = b2-4ac
Δ = 62-4·(-8)·212
Δ = 6820
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:

$\sqrt{\Delta}=\sqrt{6820}=\sqrt{4*1705}=\sqrt{4}*\sqrt{1705}=2\sqrt{1705}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{1705}}{2*-8}=\frac{-6-2\sqrt{1705}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{1705}}{2*-8}=\frac{-6+2\sqrt{1705}}{-16}
$