x/2+3x(x-1)=38

Solution for x/2+3x(x-1)=38 equation:

x/2+3x(x-1)=38

We move all terms to the left:

x/2+3x(x-1)-(38)=0

We multiply parentheses

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

We multiply all the terms by the denominator


3x^2*2+x-3x*2-38*2=0

We add all the numbers together, and all the variables

3x^2*2+x-3x*2-76=0

Wy multiply elements

6x^2+x-6x-76=0

We add all the numbers together, and all the variables

6x^2-5x-76=0

a = 6; b = -5; c = -76;
Δ = b2-4ac
Δ = -52-4·6·(-76)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-43}{2*6}=\frac{-38}{12}
=-3+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+43}{2*6}=\frac{48}{12}
=4
$