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

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

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

We move all terms to the left:

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

We multiply parentheses

-4x^2+3x+28x-(3x-8)=0

We get rid of parentheses

-4x^2+3x+28x-3x+8=0

We add all the numbers together, and all the variables

-4x^2+28x+8=0

a = -4; b = 28; c = +8;
Δ = b2-4ac
Δ = 282-4·(-4)·8
Δ = 912
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:

$\sqrt{\Delta}=\sqrt{912}=\sqrt{16*57}=\sqrt{16}*\sqrt{57}=4\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{57}}{2*-4}=\frac{-28-4\sqrt{57}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{57}}{2*-4}=\frac{-28+4\sqrt{57}}{-8}
$