(34-2x)(20-2x)=0

Solution for (34-2x)(20-2x)=0 equation:

(34-2x)(20-2x)=0

We add all the numbers together, and all the variables

(-2x+34)(-2x+20)=0

We multiply parentheses ..

(+4x^2-40x-68x+680)=0

We get rid of parentheses

4x^2-40x-68x+680=0

We add all the numbers together, and all the variables

4x^2-108x+680=0

a = 4; b = -108; c = +680;
Δ = b2-4ac
Δ = -1082-4·4·680
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-28}{2*4}=\frac{80}{8}
=10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+28}{2*4}=\frac{136}{8}
=17
$