(3x-2)x-5=15x-2

Solution for (3x-2)x-5=15x-2 equation:

(3x-2)x-5=15x-2

We move all terms to the left:

(3x-2)x-5-(15x-2)=0

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-17x-3=0

a = 3; b = -17; c = -3;
Δ = b2-4ac
Δ = -172-4·3·(-3)
Δ = 325
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:

$\sqrt{\Delta}=\sqrt{325}=\sqrt{25*13}=\sqrt{25}*\sqrt{13}=5\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-5\sqrt{13}}{2*3}=\frac{17-5\sqrt{13}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+5\sqrt{13}}{2*3}=\frac{17+5\sqrt{13}}{6}
$