X2-9-39=-2x+5

Solution for X2-9-39=-2x+5 equation:

X2-9-39=-2X+5

We move all terms to the left:

X2-9-39-(-2X+5)=0

We add all the numbers together, and all the variables

X^2-(-2X+5)-48=0

We get rid of parentheses

X^2+2X-5-48=0

We add all the numbers together, and all the variables

X^2+2X-53=0

a = 1; b = 2; c = -53;
Δ = b2-4ac
Δ = 22-4·1·(-53)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{6}}{2*1}=\frac{-2-6\sqrt{6}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{6}}{2*1}=\frac{-2+6\sqrt{6}}{2}
$