X^2+6x+2x-3=9x+27

Solution for X^2+6x+2x-3=9x+27 equation:

X^2+6X+2X-3=9X+27

We move all terms to the left:

X^2+6X+2X-3-(9X+27)=0

We add all the numbers together, and all the variables

X^2+8X-(9X+27)-3=0

We get rid of parentheses

X^2+8X-9X-27-3=0

We add all the numbers together, and all the variables

X^2-1X-30=0

a = 1; b = -1; c = -30;
Δ = b2-4ac
Δ = -12-4·1·(-30)
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{-(-1)-11}{2*1}=\frac{-10}{2}
=-5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*1}=\frac{12}{2}
=6
$