24x^2+64x=-10

Solution for 24x^2+64x=-10 equation:

24x^2+64x=-10

We move all terms to the left:

24x^2+64x-(-10)=0

We add all the numbers together, and all the variables

24x^2+64x+10=0

a = 24; b = 64; c = +10;
Δ = b2-4ac
Δ = 642-4·24·10
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-56}{2*24}=\frac{-120}{48}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+56}{2*24}=\frac{-8}{48}
=-1/6
$