8x2+21=-59x

Solution for 8x2+21=-59x equation:

8x^2+21=-59x

We move all terms to the left:

8x^2+21-(-59x)=0

We get rid of parentheses

8x^2+59x+21=0

a = 8; b = 59; c = +21;
Δ = b2-4ac
Δ = 592-4·8·21
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-53}{2*8}=\frac{-112}{16}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+53}{2*8}=\frac{-6}{16}
=-3/8
$