3x2+4x+9=180

Solution for 3x2+4x+9=180 equation:

3x^2+4x+9=180

We move all terms to the left:

3x^2+4x+9-(180)=0

We add all the numbers together, and all the variables

3x^2+4x-171=0

a = 3; b = 4; c = -171;
Δ = b2-4ac
Δ = 42-4·3·(-171)
Δ = 2068
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:

$\sqrt{\Delta}=\sqrt{2068}=\sqrt{4*517}=\sqrt{4}*\sqrt{517}=2\sqrt{517}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{517}}{2*3}=\frac{-4-2\sqrt{517}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{517}}{2*3}=\frac{-4+2\sqrt{517}}{6}
$