(8x-10)(x-2)=162

Solution for (8x-10)(x-2)=162 equation:

(8x-10)(x-2)=162

We move all terms to the left:

(8x-10)(x-2)-(162)=0

We multiply parentheses ..

(+8x^2-16x-10x+20)-162=0

We get rid of parentheses

8x^2-16x-10x+20-162=0

We add all the numbers together, and all the variables

8x^2-26x-142=0

a = 8; b = -26; c = -142;
Δ = b2-4ac
Δ = -262-4·8·(-142)
Δ = 5220
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:

$\sqrt{\Delta}=\sqrt{5220}=\sqrt{36*145}=\sqrt{36}*\sqrt{145}=6\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-6\sqrt{145}}{2*8}=\frac{26-6\sqrt{145}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+6\sqrt{145}}{2*8}=\frac{26+6\sqrt{145}}{16}
$