X^2+6x-52=3(x-8)

Solution for X^2+6x-52=3(x-8) equation:

X^2+6X-52=3(X-8)

We move all terms to the left:

X^2+6X-52-(3(X-8))=0


We calculate terms in parentheses: -(3(X-8)), so:

3(X-8)

We multiply parentheses

3X-24

Back to the equation:

-(3X-24)


We get rid of parentheses

X^2+6X-3X+24-52=0

We add all the numbers together, and all the variables

X^2+3X-28=0

a = 1; b = 3; c = -28;
Δ = b2-4ac
Δ = 32-4·1·(-28)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-11}{2*1}=\frac{-14}{2}
=-7
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+11}{2*1}=\frac{8}{2}
=4
$