(2x-1)(3x-5)-5=0

Solution for (2x-1)(3x-5)-5=0 equation:

(2x-1)(3x-5)-5=0

We multiply parentheses ..

(+6x^2-10x-3x+5)-5=0

We get rid of parentheses

6x^2-10x-3x+5-5=0

We add all the numbers together, and all the variables

6x^2-13x=0

a = 6; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·6·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*6}=\frac{26}{12}
=2+1/6
$