(2x-5)(x+1)=12x

Solution for (2x-5)(x+1)=12x equation:

(2x-5)(x+1)=12x

We move all terms to the left:

(2x-5)(x+1)-(12x)=0

We add all the numbers together, and all the variables

-12x+(2x-5)(x+1)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-15x-5=0

a = 2; b = -15; c = -5;
Δ = b2-4ac
Δ = -152-4·2·(-5)
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{-(-15)-\sqrt{265}}{2*2}=\frac{15-\sqrt{265}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{265}}{2*2}=\frac{15+\sqrt{265}}{4}
$