(x^2)/2+x=1012

Solution for (x^2)/2+x=1012 equation:

(x^2)/2+x=1012

We move all terms to the left:

(x^2)/2+x-(1012)=0

We multiply all the terms by the denominator


x^2+x*2-1012*2=0

We add all the numbers together, and all the variables

x^2+x*2-2024=0

Wy multiply elements

x^2+2x-2024=0

a = 1; b = 2; c = -2024;
Δ = b2-4ac
Δ = 22-4·1·(-2024)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-90}{2*1}=\frac{-92}{2}
=-46
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+90}{2*1}=\frac{88}{2}
=44
$