-5+3=x^2+6x-55

Solution for -5+3=x^2+6x-55 equation:

-5+3=x^2+6x-55

We move all terms to the left:

-5+3-(x^2+6x-55)=0

We add all the numbers together, and all the variables

-(x^2+6x-55)-2=0

We get rid of parentheses

-x^2-6x+55-2=0

We add all the numbers together, and all the variables

-1x^2-6x+53=0

a = -1; b = -6; c = +53;
Δ = b2-4ac
Δ = -62-4·(-1)·53
Δ = 248
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:

$\sqrt{\Delta}=\sqrt{248}=\sqrt{4*62}=\sqrt{4}*\sqrt{62}=2\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{62}}{2*-1}=\frac{6-2\sqrt{62}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{62}}{2*-1}=\frac{6+2\sqrt{62}}{-2}
$