x(x-3)/2=119

Solution for x(x-3)/2=119 equation:

x(x-3)/2=119

We move all terms to the left:

x(x-3)/2-(119)=0

We multiply all the terms by the denominator


x(x-3)-119*2=0

We add all the numbers together, and all the variables

x(x-3)-238=0

We multiply parentheses

x^2-3x-238=0

a = 1; b = -3; c = -238;
Δ = b2-4ac
Δ = -32-4·1·(-238)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-31}{2*1}=\frac{-28}{2}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+31}{2*1}=\frac{34}{2}
=17
$