-5x(4x-7)+8=3x

Solution for -5x(4x-7)+8=3x equation:

-5x(4x-7)+8=3x

We move all terms to the left:

-5x(4x-7)+8-(3x)=0

We add all the numbers together, and all the variables

-3x-5x(4x-7)+8=0

We multiply parentheses

-20x^2-3x+35x+8=0

We add all the numbers together, and all the variables

-20x^2+32x+8=0

a = -20; b = 32; c = +8;
Δ = b2-4ac
Δ = 322-4·(-20)·8
Δ = 1664
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:

$\sqrt{\Delta}=\sqrt{1664}=\sqrt{64*26}=\sqrt{64}*\sqrt{26}=8\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{26}}{2*-20}=\frac{-32-8\sqrt{26}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{26}}{2*-20}=\frac{-32+8\sqrt{26}}{-40}
$