13x^2-3x-10=90

Solution for 13x^2-3x-10=90 equation:

13x^2-3x-10=90

We move all terms to the left:

13x^2-3x-10-(90)=0

We add all the numbers together, and all the variables

13x^2-3x-100=0

a = 13; b = -3; c = -100;
Δ = b2-4ac
Δ = -32-4·13·(-100)
Δ = 5209
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{5209}}{2*13}=\frac{3-\sqrt{5209}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{5209}}{2*13}=\frac{3+\sqrt{5209}}{26}
$