8x^2+31x=-21

Solution for 8x^2+31x=-21 equation:

8x^2+31x=-21

We move all terms to the left:

8x^2+31x-(-21)=0

We add all the numbers together, and all the variables

8x^2+31x+21=0

a = 8; b = 31; c = +21;
Δ = b2-4ac
Δ = 312-4·8·21
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-17}{2*8}=\frac{-48}{16}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+17}{2*8}=\frac{-14}{16}
=-7/8
$