-8x^2-10x=-29

Solution for -8x^2-10x=-29 equation:

-8x^2-10x=-29

We move all terms to the left:

-8x^2-10x-(-29)=0

We add all the numbers together, and all the variables

-8x^2-10x+29=0

a = -8; b = -10; c = +29;
Δ = b2-4ac
Δ = -102-4·(-8)·29
Δ = 1028
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1028}=\sqrt{4*257}=\sqrt{4}*\sqrt{257}=2\sqrt{257}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{257}}{2*-8}=\frac{10-2\sqrt{257}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{257}}{2*-8}=\frac{10+2\sqrt{257}}{-16}
$