2x^2+13x=10

Solution for 2x^2+13x=10 equation:

2x^2+13x=10

We move all terms to the left:

2x^2+13x-(10)=0

a = 2; b = 13; c = -10;
Δ = b2-4ac
Δ = 132-4·2·(-10)
Δ = 249
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{249}}{2*2}=\frac{-13-\sqrt{249}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{249}}{2*2}=\frac{-13+\sqrt{249}}{4}
$