3x+10x2=180

Solution for 3x+10x2=180 equation:

3x+10x^2=180

We move all terms to the left:

3x+10x^2-(180)=0

a = 10; b = 3; c = -180;
Δ = b2-4ac
Δ = 32-4·10·(-180)
Δ = 7209
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:

$\sqrt{\Delta}=\sqrt{7209}=\sqrt{81*89}=\sqrt{81}*\sqrt{89}=9\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9\sqrt{89}}{2*10}=\frac{-3-9\sqrt{89}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9\sqrt{89}}{2*10}=\frac{-3+9\sqrt{89}}{20}
$