(3x+50)(x+10)=180

Solution for (3x+50)(x+10)=180 equation:

(3x+50)(x+10)=180

We move all terms to the left:

(3x+50)(x+10)-(180)=0

We multiply parentheses ..

(+3x^2+30x+50x+500)-180=0

We get rid of parentheses

3x^2+30x+50x+500-180=0

We add all the numbers together, and all the variables

3x^2+80x+320=0

a = 3; b = 80; c = +320;
Δ = b2-4ac
Δ = 802-4·3·320
Δ = 2560
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:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-16\sqrt{10}}{2*3}=\frac{-80-16\sqrt{10}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+16\sqrt{10}}{2*3}=\frac{-80+16\sqrt{10}}{6}
$