(7-2x)(3-2x)=6

Solution for (7-2x)(3-2x)=6 equation:

(7-2x)(3-2x)=6

We move all terms to the left:

(7-2x)(3-2x)-(6)=0

We add all the numbers together, and all the variables

(-2x+7)(-2x+3)-6=0

We multiply parentheses ..

(+4x^2-6x-14x+21)-6=0

We get rid of parentheses

4x^2-6x-14x+21-6=0

We add all the numbers together, and all the variables

4x^2-20x+15=0

a = 4; b = -20; c = +15;
Δ = b2-4ac
Δ = -202-4·4·15
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{10}}{2*4}=\frac{20-4\sqrt{10}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{10}}{2*4}=\frac{20+4\sqrt{10}}{8}
$