(12-2x)(10-2x)=x

Solution for (12-2x)(10-2x)=x equation:

(12-2x)(10-2x)=x

We move all terms to the left:

(12-2x)(10-2x)-(x)=0

We add all the numbers together, and all the variables

(-2x+12)(-2x+10)-x=0

We add all the numbers together, and all the variables

-1x+(-2x+12)(-2x+10)=0

We multiply parentheses ..

(+4x^2-20x-24x+120)-1x=0

We get rid of parentheses

4x^2-20x-24x-1x+120=0

We add all the numbers together, and all the variables

4x^2-45x+120=0

a = 4; b = -45; c = +120;
Δ = b2-4ac
Δ = -452-4·4·120
Δ = 105
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{-(-45)-\sqrt{105}}{2*4}=\frac{45-\sqrt{105}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{105}}{2*4}=\frac{45+\sqrt{105}}{8}
$