5x+12=2x(x-4)

Solution for 5x+12=2x(x-4) equation:

5x+12=2x(x-4)

We move all terms to the left:

5x+12-(2x(x-4))=0


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

2x(x-4)

We multiply parentheses

2x^2-8x

Back to the equation:

-(2x^2-8x)


We get rid of parentheses

-2x^2+5x+8x+12=0

We add all the numbers together, and all the variables

-2x^2+13x+12=0

a = -2; b = 13; c = +12;
Δ = b2-4ac
Δ = 132-4·(-2)·12
Δ = 265
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{-(13)-\sqrt{265}}{2*-2}=\frac{-13-\sqrt{265}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{265}}{2*-2}=\frac{-13+\sqrt{265}}{-4}
$