(15-2x)*(6-2x)=420

Solution for (15-2x)*(6-2x)=420 equation:

(15-2x)(6-2x)=420

We move all terms to the left:

(15-2x)(6-2x)-(420)=0

We add all the numbers together, and all the variables

(-2x+15)(-2x+6)-420=0

We multiply parentheses ..

(+4x^2-12x-30x+90)-420=0

We get rid of parentheses

4x^2-12x-30x+90-420=0

We add all the numbers together, and all the variables

4x^2-42x-330=0

a = 4; b = -42; c = -330;
Δ = b2-4ac
Δ = -422-4·4·(-330)
Δ = 7044
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:

$\sqrt{\Delta}=\sqrt{7044}=\sqrt{4*1761}=\sqrt{4}*\sqrt{1761}=2\sqrt{1761}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{1761}}{2*4}=\frac{42-2\sqrt{1761}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{1761}}{2*4}=\frac{42+2\sqrt{1761}}{8}
$