2x^2+16x=-21

Solution for 2x^2+16x=-21 equation:

2x^2+16x=-21

We move all terms to the left:

2x^2+16x-(-21)=0

We add all the numbers together, and all the variables

2x^2+16x+21=0

a = 2; b = 16; c = +21;
Δ = b2-4ac
Δ = 162-4·2·21
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{22}}{2*2}=\frac{-16-2\sqrt{22}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{22}}{2*2}=\frac{-16+2\sqrt{22}}{4}
$