9x^2-138x-320=0

Solution for 9x^2-138x-320=0 equation:

9x^2-138x-320=0

a = 9; b = -138; c = -320;
Δ = b2-4ac
Δ = -1382-4·9·(-320)
Δ = 30564
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:

$\sqrt{\Delta}=\sqrt{30564}=\sqrt{36*849}=\sqrt{36}*\sqrt{849}=6\sqrt{849}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-138)-6\sqrt{849}}{2*9}=\frac{138-6\sqrt{849}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-138)+6\sqrt{849}}{2*9}=\frac{138+6\sqrt{849}}{18}
$