(3/2x)+4=2x-5

Solution for (3/2x)+4=2x-5 equation:

(3/2x)+4=2x-5

We move all terms to the left:

(3/2x)+4-(2x-5)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/2x)-(2x-5)+4=0

We get rid of parentheses

3/2x-2x+5+4=0

We multiply all the terms by the denominator


-2x*2x+5*2x+4*2x+3=0

Wy multiply elements

-4x^2+10x+8x+3=0

We add all the numbers together, and all the variables

-4x^2+18x+3=0

a = -4; b = 18; c = +3;
Δ = b2-4ac
Δ = 182-4·(-4)·3
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{93}}{2*-4}=\frac{-18-2\sqrt{93}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{93}}{2*-4}=\frac{-18+2\sqrt{93}}{-8}
$