x(3x+10)=180

Solution for x(3x+10)=180 equation:

x(3x+10)=180

We move all terms to the left:

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

We multiply parentheses

3x^2+10x-180=0

a = 3; b = 10; c = -180;
Δ = b2-4ac
Δ = 102-4·3·(-180)
Δ = 2260
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:

$\sqrt{\Delta}=\sqrt{2260}=\sqrt{4*565}=\sqrt{4}*\sqrt{565}=2\sqrt{565}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{565}}{2*3}=\frac{-10-2\sqrt{565}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{565}}{2*3}=\frac{-10+2\sqrt{565}}{6}
$