6x^2+9x=27

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

6x^2+9x=27

We move all terms to the left:

6x^2+9x-(27)=0

a = 6; b = 9; c = -27;
Δ = b2-4ac
Δ = 92-4·6·(-27)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-27}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+27}{2*6}=\frac{18}{12}
=1+1/2
$