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 = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{21}}{2*-3}=\frac{-15-3\sqrt{21}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{21}}{2*-3}=\frac{-15+3\sqrt{21}}{-6}
$