(5x-17)(2x+50)=180

Solution for (5x-17)(2x+50)=180 equation:

(5x-17)(2x+50)=180

We move all terms to the left:

(5x-17)(2x+50)-(180)=0

We multiply parentheses ..

(+10x^2+250x-34x-850)-180=0

We get rid of parentheses

10x^2+250x-34x-850-180=0

We add all the numbers together, and all the variables

10x^2+216x-1030=0

a = 10; b = 216; c = -1030;
Δ = b2-4ac
Δ = 2162-4·10·(-1030)
Δ = 87856
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:

$\sqrt{\Delta}=\sqrt{87856}=\sqrt{4624*19}=\sqrt{4624}*\sqrt{19}=68\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-68\sqrt{19}}{2*10}=\frac{-216-68\sqrt{19}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+68\sqrt{19}}{2*10}=\frac{-216+68\sqrt{19}}{20}
$