(14-2x)(20-2x)=190

Solution for (14-2x)(20-2x)=190 equation:

(14-2x)(20-2x)=190

We move all terms to the left:

(14-2x)(20-2x)-(190)=0

We add all the numbers together, and all the variables

(-2x+14)(-2x+20)-190=0

We multiply parentheses ..

(+4x^2-40x-28x+280)-190=0

We get rid of parentheses

4x^2-40x-28x+280-190=0

We add all the numbers together, and all the variables

4x^2-68x+90=0

a = 4; b = -68; c = +90;
Δ = b2-4ac
Δ = -682-4·4·90
Δ = 3184
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:

$\sqrt{\Delta}=\sqrt{3184}=\sqrt{16*199}=\sqrt{16}*\sqrt{199}=4\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-4\sqrt{199}}{2*4}=\frac{68-4\sqrt{199}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+4\sqrt{199}}{2*4}=\frac{68+4\sqrt{199}}{8}
$