X^2+8x+7=107

Solution for X^2+8x+7=107 equation:

X^2+8X+7=107

We move all terms to the left:

X^2+8X+7-(107)=0

We add all the numbers together, and all the variables

X^2+8X-100=0

a = 1; b = 8; c = -100;
Δ = b2-4ac
Δ = 82-4·1·(-100)
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{29}}{2*1}=\frac{-8-4\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{29}}{2*1}=\frac{-8+4\sqrt{29}}{2}
$