(3x+17)(1/2x-5)=180

Solution for (3x+17)(1/2x-5)=180 equation:

(3x+17)(1/2x-5)=180

We move all terms to the left:

(3x+17)(1/2x-5)-(180)=0


Domain of the equation: 2x-5)!=0

x∈R


We multiply parentheses ..

(+3x^2-15x+17x-85)-180=0

We get rid of parentheses

3x^2-15x+17x-85-180=0

We add all the numbers together, and all the variables

3x^2+2x-265=0

a = 3; b = 2; c = -265;
Δ = b2-4ac
Δ = 22-4·3·(-265)
Δ = 3184
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:

$\sqrt{\Delta}=\sqrt{3184}=\sqrt{16*199}=\sqrt{16}*\sqrt{199}=4\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{199}}{2*3}=\frac{-2-4\sqrt{199}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{199}}{2*3}=\frac{-2+4\sqrt{199}}{6}
$