X^2+6x-12+3=x-5

Solution for X^2+6x-12+3=x-5 equation:

X^2+6X-12+3=X-5

We move all terms to the left:

X^2+6X-12+3-(X-5)=0

We add all the numbers together, and all the variables

X^2+6X-(X-5)-9=0

We get rid of parentheses

X^2+6X-X+5-9=0

We add all the numbers together, and all the variables

X^2+5X-4=0

a = 1; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·1·(-4)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{41}}{2*1}=\frac{-5-\sqrt{41}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{41}}{2*1}=\frac{-5+\sqrt{41}}{2}
$