8x^2-10=-13x

Solution for 8x^2-10=-13x equation:

8x^2-10=-13x

We move all terms to the left:

8x^2-10-(-13x)=0

We get rid of parentheses

8x^2+13x-10=0

a = 8; b = 13; c = -10;
Δ = b2-4ac
Δ = 132-4·8·(-10)
Δ = 489
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{489}}{2*8}=\frac{-13-\sqrt{489}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{489}}{2*8}=\frac{-13+\sqrt{489}}{16}
$