(X^2)/2+2x=216

Solution for (X^2)/2+2x=216 equation:

(X^2)/2+2X=216

We move all terms to the left:

(X^2)/2+2X-(216)=0

We multiply all the terms by the denominator


X^2+2X*2-216*2=0

We add all the numbers together, and all the variables

X^2+2X*2-432=0

Wy multiply elements

X^2+4X-432=0

a = 1; b = 4; c = -432;
Δ = b2-4ac
Δ = 42-4·1·(-432)
Δ = 1744
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:

$\sqrt{\Delta}=\sqrt{1744}=\sqrt{16*109}=\sqrt{16}*\sqrt{109}=4\sqrt{109}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{109}}{2*1}=\frac{-4-4\sqrt{109}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{109}}{2*1}=\frac{-4+4\sqrt{109}}{2}
$