(x-8)(x-10)=50

Solution for (x-8)(x-10)=50 equation:

(x-8)(x-10)=50

We move all terms to the left:

(x-8)(x-10)-(50)=0

We multiply parentheses ..

(+x^2-10x-8x+80)-50=0

We get rid of parentheses

x^2-10x-8x+80-50=0

We add all the numbers together, and all the variables

x^2-18x+30=0

a = 1; b = -18; c = +30;
Δ = b2-4ac
Δ = -182-4·1·30
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{51}}{2*1}=\frac{18-2\sqrt{51}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{51}}{2*1}=\frac{18+2\sqrt{51}}{2}
$