(X-17)(5x-1)=180

Solution for (X-17)(5x-1)=180 equation:

(X-17)(5X-1)=180

We move all terms to the left:

(X-17)(5X-1)-(180)=0

We multiply parentheses ..

(+5X^2-1X-85X+17)-180=0

We get rid of parentheses

5X^2-1X-85X+17-180=0

We add all the numbers together, and all the variables

5X^2-86X-163=0

a = 5; b = -86; c = -163;
Δ = b2-4ac
Δ = -862-4·5·(-163)
Δ = 10656
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:

$\sqrt{\Delta}=\sqrt{10656}=\sqrt{144*74}=\sqrt{144}*\sqrt{74}=12\sqrt{74}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-12\sqrt{74}}{2*5}=\frac{86-12\sqrt{74}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+12\sqrt{74}}{2*5}=\frac{86+12\sqrt{74}}{10}
$