9x^2+6x=77

Solution for 9x^2+6x=77 equation:

9x^2+6x=77

We move all terms to the left:

9x^2+6x-(77)=0

a = 9; b = 6; c = -77;
Δ = b2-4ac
Δ = 62-4·9·(-77)
Δ = 2808
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:

$\sqrt{\Delta}=\sqrt{2808}=\sqrt{36*78}=\sqrt{36}*\sqrt{78}=6\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{78}}{2*9}=\frac{-6-6\sqrt{78}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{78}}{2*9}=\frac{-6+6\sqrt{78}}{18}
$