(12-2x)*(5-2x)=30

Solution for (12-2x)*(5-2x)=30 equation:

(12-2x)(5-2x)=30

We move all terms to the left:

(12-2x)(5-2x)-(30)=0

We add all the numbers together, and all the variables

(-2x+12)(-2x+5)-30=0

We multiply parentheses ..

(+4x^2-10x-24x+60)-30=0

We get rid of parentheses

4x^2-10x-24x+60-30=0

We add all the numbers together, and all the variables

4x^2-34x+30=0

a = 4; b = -34; c = +30;
Δ = b2-4ac
Δ = -342-4·4·30
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-26}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+26}{2*4}=\frac{60}{8}
=7+1/2
$