3/2x+6=2x-1

Solution for 3/2x+6=2x-1 equation:

3/2x+6=2x-1

We move all terms to the left:

3/2x+6-(2x-1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-2x+1+6=0

We multiply all the terms by the denominator


-2x*2x+1*2x+6*2x+3=0

Wy multiply elements

-4x^2+2x+12x+3=0

We add all the numbers together, and all the variables

-4x^2+14x+3=0

a = -4; b = 14; c = +3;
Δ = b2-4ac
Δ = 142-4·(-4)·3
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{61}}{2*-4}=\frac{-14-2\sqrt{61}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{61}}{2*-4}=\frac{-14+2\sqrt{61}}{-8}
$