X/2+3x^2-x=0

Solution for X/2+3x^2-x=0 equation:

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

We add all the numbers together, and all the variables

3X^2-1X+X/2=0

We multiply all the terms by the denominator


3X^2*2-1X*2+X=0

We add all the numbers together, and all the variables

3X^2*2+X-1X*2=0

Wy multiply elements

6X^2+X-2X=0

We add all the numbers together, and all the variables

6X^2-1X=0

a = 6; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·6·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*6}=\frac{0}{12}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*6}=\frac{2}{12}
=1/6
$