(x-3)(x)/2=35

Solution for (x-3)(x)/2=35 equation:

(x-3)(x)/2=35

We move all terms to the left:

(x-3)(x)/2-(35)=0

We multiply all the terms by the denominator


(x-3)x-35*2=0

We add all the numbers together, and all the variables

(x-3)x-70=0

We multiply parentheses

x^2-3x-70=0

a = 1; b = -3; c = -70;
Δ = b2-4ac
Δ = -32-4·1·(-70)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-17}{2*1}=\frac{-14}{2}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+17}{2*1}=\frac{20}{2}
=10
$