x/2+3x^2-3=38

Solution for x/2+3x^2-3=38 equation:

x/2+3x^2-3=38

We move all terms to the left:

x/2+3x^2-3-(38)=0

We add all the numbers together, and all the variables

3x^2+x/2-41=0

We multiply all the terms by the denominator


3x^2*2+x-41*2=0

We add all the numbers together, and all the variables

3x^2*2+x-82=0

Wy multiply elements

6x^2+x-82=0

a = 6; b = 1; c = -82;
Δ = b2-4ac
Δ = 12-4·6·(-82)
Δ = 1969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{1969}}{2*6}=\frac{-1-\sqrt{1969}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1969}}{2*6}=\frac{-1+\sqrt{1969}}{12}
$