2x^2-15x+31=13

Solution for 2x^2-15x+31=13 equation:

2x^2-15x+31=13

We move all terms to the left:

2x^2-15x+31-(13)=0

We add all the numbers together, and all the variables

2x^2-15x+18=0

a = 2; b = -15; c = +18;
Δ = b2-4ac
Δ = -152-4·2·18
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-9}{2*2}=\frac{6}{4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+9}{2*2}=\frac{24}{4}
=6
$