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 add all the numbers together, and all the variables

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+x-6=0

Wy multiply elements

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