X^2-85=-4x-14

Solution for X^2-85=-4x-14 equation:

X^2-85=-4X-14

We move all terms to the left:

X^2-85-(-4X-14)=0

We get rid of parentheses

X^2+4X+14-85=0

We add all the numbers together, and all the variables

X^2+4X-71=0

a = 1; b = 4; c = -71;
Δ = b2-4ac
Δ = 42-4·1·(-71)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-10\sqrt{3}}{2*1}=\frac{-4-10\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+10\sqrt{3}}{2*1}=\frac{-4+10\sqrt{3}}{2}
$