7x^2-13x=2

Solution for 7x^2-13x=2 equation:

7x^2-13x=2

We move all terms to the left:

7x^2-13x-(2)=0

a = 7; b = -13; c = -2;
Δ = b2-4ac
Δ = -132-4·7·(-2)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-15}{2*7}=\frac{-2}{14}
=-1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+15}{2*7}=\frac{28}{14}
=2
$