(X^2-22)=(6x+5)

Solution for (X^2-22)=(6x+5) equation:

(X^2-22)=(6X+5)

We move all terms to the left:

(X^2-22)-((6X+5))=0

We get rid of parentheses

X^2-((6X+5))-22=0


We calculate terms in parentheses: -((6X+5)), so:

(6X+5)

We get rid of parentheses

6X+5

Back to the equation:

-(6X+5)


We get rid of parentheses

X^2-6X-5-22=0

We add all the numbers together, and all the variables

X^2-6X-27=0

a = 1; b = -6; c = -27;
Δ = b2-4ac
Δ = -62-4·1·(-27)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12}{2*1}=\frac{-6}{2}
=-3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12}{2*1}=\frac{18}{2}
=9
$