(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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-17x=0

a = 2; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·2·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*2}=\frac{34}{4}
=8+1/2
$