(3x+17)(.5x-5)=90

Solution for (3x+17)(.5x-5)=90 equation:

(3x+17)(.5x-5)=90

We move all terms to the left:

(3x+17)(.5x-5)-(90)=0

We multiply parentheses ..

(+3x^2-15x+17x-85)-90=0

We get rid of parentheses

3x^2-15x+17x-85-90=0

We add all the numbers together, and all the variables

3x^2+2x-175=0

a = 3; b = 2; c = -175;
Δ = b2-4ac
Δ = 22-4·3·(-175)
Δ = 2104
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:

$\sqrt{\Delta}=\sqrt{2104}=\sqrt{4*526}=\sqrt{4}*\sqrt{526}=2\sqrt{526}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{526}}{2*3}=\frac{-2-2\sqrt{526}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{526}}{2*3}=\frac{-2+2\sqrt{526}}{6}
$