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