4x+6x2=180

Solution for 4x+6x2=180 equation:

4x+6x^2=180

We move all terms to the left:

4x+6x^2-(180)=0

a = 6; b = 4; c = -180;
Δ = b2-4ac
Δ = 42-4·6·(-180)
Δ = 4336
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:

$\sqrt{\Delta}=\sqrt{4336}=\sqrt{16*271}=\sqrt{16}*\sqrt{271}=4\sqrt{271}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{271}}{2*6}=\frac{-4-4\sqrt{271}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{271}}{2*6}=\frac{-4+4\sqrt{271}}{12}
$