X*X/2+4x=64

Solution for X*X/2+4x=64 equation:

X*X/2+4X=64

We move all terms to the left:

X*X/2+4X-(64)=0

We add all the numbers together, and all the variables

4X+X*X/2-64=0

We multiply all the terms by the denominator


4X*2+X*X-64*2=0

We add all the numbers together, and all the variables

4X*2+X*X-128=0

Wy multiply elements

X^2+8X-128=0

a = 1; b = 8; c = -128;
Δ = b2-4ac
Δ = 82-4·1·(-128)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-24}{2*1}=\frac{-32}{2}
=-16
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+24}{2*1}=\frac{16}{2}
=8
$