9x^2+8x^2+6x=180

Solution for 9x^2+8x^2+6x=180 equation:

9x^2+8x^2+6x=180

We move all terms to the left:

9x^2+8x^2+6x-(180)=0

We add all the numbers together, and all the variables

17x^2+6x-180=0

a = 17; b = 6; c = -180;
Δ = b2-4ac
Δ = 62-4·17·(-180)
Δ = 12276
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:

$\sqrt{\Delta}=\sqrt{12276}=\sqrt{36*341}=\sqrt{36}*\sqrt{341}=6\sqrt{341}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{341}}{2*17}=\frac{-6-6\sqrt{341}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{341}}{2*17}=\frac{-6+6\sqrt{341}}{34}
$