X^2+2x+6=-x^2+7x+123

Solution for X^2+2x+6=-x^2+7x+123 equation:

X^2+2X+6=-X^2+7X+123

We move all terms to the left:

X^2+2X+6-(-X^2+7X+123)=0

We get rid of parentheses

X^2+X^2-7X+2X-123+6=0

We add all the numbers together, and all the variables

2X^2-5X-117=0

a = 2; b = -5; c = -117;
Δ = b2-4ac
Δ = -52-4·2·(-117)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-31}{2*2}=\frac{-26}{4}
=-6+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+31}{2*2}=\frac{36}{4}
=9
$