2+3x(x-5)=5

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

2+3x(x-5)=5

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x(x-5)-3=0

We multiply parentheses

3x^2-15x-3=0

a = 3; b = -15; c = -3;
Δ = b2-4ac
Δ = -152-4·3·(-3)
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{29}}{2*3}=\frac{15-3\sqrt{29}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{29}}{2*3}=\frac{15+3\sqrt{29}}{6}
$