(60+10x)(17x+11)=180

Solution for (60+10x)(17x+11)=180 equation:

(60+10x)(17x+11)=180

We move all terms to the left:

(60+10x)(17x+11)-(180)=0

We add all the numbers together, and all the variables

(10x+60)(17x+11)-180=0

We multiply parentheses ..

(+170x^2+110x+1020x+660)-180=0

We get rid of parentheses

170x^2+110x+1020x+660-180=0

We add all the numbers together, and all the variables

170x^2+1130x+480=0

a = 170; b = 1130; c = +480;
Δ = b2-4ac
Δ = 11302-4·170·480
Δ = 950500
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:

$\sqrt{\Delta}=\sqrt{950500}=\sqrt{100*9505}=\sqrt{100}*\sqrt{9505}=10\sqrt{9505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1130)-10\sqrt{9505}}{2*170}=\frac{-1130-10\sqrt{9505}}{340}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1130)+10\sqrt{9505}}{2*170}=\frac{-1130+10\sqrt{9505}}{340}
$