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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+3x^2+150x+10x+500)-180=0

We get rid of parentheses

3x^2+150x+10x+500-180=0

We add all the numbers together, and all the variables

3x^2+160x+320=0

a = 3; b = 160; c = +320;
Δ = b2-4ac
Δ = 1602-4·3·320
Δ = 21760
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:

$\sqrt{\Delta}=\sqrt{21760}=\sqrt{256*85}=\sqrt{256}*\sqrt{85}=16\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-16\sqrt{85}}{2*3}=\frac{-160-16\sqrt{85}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+16\sqrt{85}}{2*3}=\frac{-160+16\sqrt{85}}{6}
$