(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^2-19x+5=0

a = 2; b = -19; c = +5;
Δ = b2-4ac
Δ = -192-4·2·5
Δ = 321
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{-(-19)-\sqrt{321}}{2*2}=\frac{19-\sqrt{321}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{321}}{2*2}=\frac{19+\sqrt{321}}{4}
$