X^2=x/2+3

Solution for X^2=x/2+3 equation:

X^2=X/2+3

We move all terms to the left:

X^2-(X/2+3)=0

We get rid of parentheses

X^2-X/2-3=0

We multiply all the terms by the denominator


X^2*2-X-3*2=0

We add all the numbers together, and all the variables

X^2*2-1X-6=0

Wy multiply elements

2X^2-1X-6=0

a = 2; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·2·(-6)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-7}{2*2}=\frac{-6}{4}
=-1+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*2}=\frac{8}{4}
=2
$