R(x)=3x-3/2x-4

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

(R)=3R-3/2R-4

We move all terms to the left:

(R)-(3R-3/2R-4)=0


Domain of the equation: 2R-4)!=0

R∈R


We get rid of parentheses

R-3R+3/2R+4=0

We multiply all the terms by the denominator


R*2R-3R*2R+4*2R+3=0

Wy multiply elements

2R^2-6R^2+8R+3=0

We add all the numbers together, and all the variables

-4R^2+8R+3=0

a = -4; b = 8; c = +3;
Δ = b2-4ac
Δ = 82-4·(-4)·3
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{7}}{2*-4}=\frac{-8-4\sqrt{7}}{-8}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{7}}{2*-4}=\frac{-8+4\sqrt{7}}{-8}
$