(34-2x)(10-2x)=180

Solution for (34-2x)(10-2x)=180 equation:

(34-2x)(10-2x)=180

We move all terms to the left:

(34-2x)(10-2x)-(180)=0

We add all the numbers together, and all the variables

(-2x+34)(-2x+10)-180=0

We multiply parentheses ..

(+4x^2-20x-68x+340)-180=0

We get rid of parentheses

4x^2-20x-68x+340-180=0

We add all the numbers together, and all the variables

4x^2-88x+160=0

a = 4; b = -88; c = +160;
Δ = b2-4ac
Δ = -882-4·4·160
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-72}{2*4}=\frac{16}{8}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+72}{2*4}=\frac{160}{8}
=20
$