X^2+4x+5=-6x+8

Solution for X^2+4x+5=-6x+8 equation:

X^2+4X+5=-6X+8

We move all terms to the left:

X^2+4X+5-(-6X+8)=0

We get rid of parentheses

X^2+4X+6X-8+5=0

We add all the numbers together, and all the variables

X^2+10X-3=0

a = 1; b = 10; c = -3;
Δ = b2-4ac
Δ = 102-4·1·(-3)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{7}}{2*1}=\frac{-10-4\sqrt{7}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{7}}{2*1}=\frac{-10+4\sqrt{7}}{2}
$