7x^2-9x=-2

Solution for 7x^2-9x=-2 equation:

7x^2-9x=-2

We move all terms to the left:

7x^2-9x-(-2)=0

We add all the numbers together, and all the variables

7x^2-9x+2=0

a = 7; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·7·2
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-5}{2*7}=\frac{4}{14}
=2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+5}{2*7}=\frac{14}{14}
=1
$