(3x-5)(x-5)=30

Solution for (3x-5)(x-5)=30 equation:

(3x-5)(x-5)=30

We move all terms to the left:

(3x-5)(x-5)-(30)=0

We multiply parentheses ..

(+3x^2-15x-5x+25)-30=0

We get rid of parentheses

3x^2-15x-5x+25-30=0

We add all the numbers together, and all the variables

3x^2-20x-5=0

a = 3; b = -20; c = -5;
Δ = b2-4ac
Δ = -202-4·3·(-5)
Δ = 460
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:

$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{115}}{2*3}=\frac{20-2\sqrt{115}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{115}}{2*3}=\frac{20+2\sqrt{115}}{6}
$