8x(x-1)=7x2+4x

Solution for 8x(x-1)=7x2+4x equation:

8x(x-1)=7x^2+4x

We move all terms to the left:

8x(x-1)-(7x^2+4x)=0

We multiply parentheses

8x^2-8x-(7x^2+4x)=0

We get rid of parentheses

8x^2-7x^2-8x-4x=0

We add all the numbers together, and all the variables

x^2-12x=0

a = 1; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·1·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*1}=\frac{24}{2}
=12
$