2x^2-13x+5=8

Solution for 2x^2-13x+5=8 equation:

2x^2-13x+5=8

We move all terms to the left:

2x^2-13x+5-(8)=0

We add all the numbers together, and all the variables

2x^2-13x-3=0

a = 2; b = -13; c = -3;
Δ = b2-4ac
Δ = -132-4·2·(-3)
Δ = 193
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{-(-13)-\sqrt{193}}{2*2}=\frac{13-\sqrt{193}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{193}}{2*2}=\frac{13+\sqrt{193}}{4}
$