6x^2-13x+5=90

Solution for 6x^2-13x+5=90 equation:

6x^2-13x+5=90

We move all terms to the left:

6x^2-13x+5-(90)=0

We add all the numbers together, and all the variables

6x^2-13x-85=0

a = 6; b = -13; c = -85;
Δ = b2-4ac
Δ = -132-4·6·(-85)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-47}{2*6}=\frac{-34}{12}
=-2+5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+47}{2*6}=\frac{60}{12}
=5
$