7x^2-66x=-27

Solution for 7x^2-66x=-27 equation:

7x^2-66x=-27

We move all terms to the left:

7x^2-66x-(-27)=0

We add all the numbers together, and all the variables

7x^2-66x+27=0

a = 7; b = -66; c = +27;
Δ = b2-4ac
Δ = -662-4·7·27
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-60}{2*7}=\frac{6}{14}
=3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+60}{2*7}=\frac{126}{14}
=9
$