7x^2+24x=9

Solution for 7x^2+24x=9 equation:

7x^2+24x=9

We move all terms to the left:

7x^2+24x-(9)=0

a = 7; b = 24; c = -9;
Δ = b2-4ac
Δ = 242-4·7·(-9)
Δ = 828
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:

$\sqrt{\Delta}=\sqrt{828}=\sqrt{36*23}=\sqrt{36}*\sqrt{23}=6\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{23}}{2*7}=\frac{-24-6\sqrt{23}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{23}}{2*7}=\frac{-24+6\sqrt{23}}{14}
$