(4x-10)(x-2)=80

Solution for (4x-10)(x-2)=80 equation:

(4x-10)(x-2)=80

We move all terms to the left:

(4x-10)(x-2)-(80)=0

We multiply parentheses ..

(+4x^2-8x-10x+20)-80=0

We get rid of parentheses

4x^2-8x-10x+20-80=0

We add all the numbers together, and all the variables

4x^2-18x-60=0

a = 4; b = -18; c = -60;
Δ = b2-4ac
Δ = -182-4·4·(-60)
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{321}}{2*4}=\frac{18-2\sqrt{321}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{321}}{2*4}=\frac{18+2\sqrt{321}}{8}
$