(5x-3)(x-3)=8

Solution for (5x-3)(x-3)=8 equation:

(5x-3)(x-3)=8

We move all terms to the left:

(5x-3)(x-3)-(8)=0

We multiply parentheses ..

(+5x^2-15x-3x+9)-8=0

We get rid of parentheses

5x^2-15x-3x+9-8=0

We add all the numbers together, and all the variables

5x^2-18x+1=0

a = 5; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·5·1
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4\sqrt{19}}{2*5}=\frac{18-4\sqrt{19}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4\sqrt{19}}{2*5}=\frac{18+4\sqrt{19}}{10}
$