x(x-3)/2=170

Solution for x(x-3)/2=170 equation:

x(x-3)/2=170

We move all terms to the left:

x(x-3)/2-(170)=0

We multiply all the terms by the denominator


x(x-3)-170*2=0

We add all the numbers together, and all the variables

x(x-3)-340=0

We multiply parentheses

x^2-3x-340=0

a = 1; b = -3; c = -340;
Δ = b2-4ac
Δ = -32-4·1·(-340)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-37}{2*1}=\frac{-34}{2}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+37}{2*1}=\frac{40}{2}
=20
$