5-8x-4x^2=-10

Solution for 5-8x-4x^2=-10 equation:

5-8x-4x^2=-10

We move all terms to the left:

5-8x-4x^2-(-10)=0

We add all the numbers together, and all the variables

-4x^2-8x+15=0

a = -4; b = -8; c = +15;
Δ = b2-4ac
Δ = -82-4·(-4)·15
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{19}}{2*-4}=\frac{8-4\sqrt{19}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{19}}{2*-4}=\frac{8+4\sqrt{19}}{-8}
$