15=5x^2-3x+2

Solution for 15=5x^2-3x+2 equation:

15=5x^2-3x+2

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5x^2+3x+13=0

a = -5; b = 3; c = +13;
Δ = b2-4ac
Δ = 32-4·(-5)·13
Δ = 269
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{269}}{2*-5}=\frac{-3-\sqrt{269}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{269}}{2*-5}=\frac{-3+\sqrt{269}}{-10}
$