X2-92=-16x

Solution for X2-92=-16x equation:

X2-92=-16X

We move all terms to the left:

X2-92-(-16X)=0

We add all the numbers together, and all the variables

X^2-(-16X)-92=0

We get rid of parentheses

X^2+16X-92=0

a = 1; b = 16; c = -92;
Δ = b2-4ac
Δ = 162-4·1·(-92)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{39}}{2*1}=\frac{-16-4\sqrt{39}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{39}}{2*1}=\frac{-16+4\sqrt{39}}{2}
$