-3x+(1/2x-1)=4

Solution for -3x+(1/2x-1)=4 equation:

-3x+(1/2x-1)=4

We move all terms to the left:

-3x+(1/2x-1)-(4)=0


Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

-3x+1/2x-1-4=0

We multiply all the terms by the denominator


-3x*2x-1*2x-4*2x+1=0

Wy multiply elements

-6x^2-2x-8x+1=0

We add all the numbers together, and all the variables

-6x^2-10x+1=0

a = -6; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·(-6)·1
Δ = 124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{31}}{2*-6}=\frac{10-2\sqrt{31}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{31}}{2*-6}=\frac{10+2\sqrt{31}}{-12}
$