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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-14x+10=0

a = 3; b = -14; c = +10;
Δ = b2-4ac
Δ = -142-4·3·10
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{19}}{2*3}=\frac{14-2\sqrt{19}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{19}}{2*3}=\frac{14+2\sqrt{19}}{6}
$