7x^2+9x=23

Solution for 7x^2+9x=23 equation:

7x^2+9x=23

We move all terms to the left:

7x^2+9x-(23)=0

a = 7; b = 9; c = -23;
Δ = b2-4ac
Δ = 92-4·7·(-23)
Δ = 725
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{725}=\sqrt{25*29}=\sqrt{25}*\sqrt{29}=5\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-5\sqrt{29}}{2*7}=\frac{-9-5\sqrt{29}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+5\sqrt{29}}{2*7}=\frac{-9+5\sqrt{29}}{14}
$