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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+2x^2+3x-8x-12)-4x=0

We get rid of parentheses

2x^2+3x-8x-4x-12=0

We add all the numbers together, and all the variables

2x^2-9x-12=0

a = 2; b = -9; c = -12;
Δ = b2-4ac
Δ = -92-4·2·(-12)
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{177}}{2*2}=\frac{9-\sqrt{177}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{177}}{2*2}=\frac{9+\sqrt{177}}{4}
$