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

a = 7; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·7·(-2)
Δ = 137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{137}}{2*7}=\frac{-9-\sqrt{137}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{137}}{2*7}=\frac{-9+\sqrt{137}}{14}
$