x+3/2x-4=5

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

X+3/2X-4=5

We move all terms to the left:

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


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

X+3/2X-9=0

We multiply all the terms by the denominator


X*2X-9*2X+3=0

Wy multiply elements

2X^2-18X+3=0

a = 2; b = -18; c = +3;
Δ = b2-4ac
Δ = -182-4·2·3
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-10\sqrt{3}}{2*2}=\frac{18-10\sqrt{3}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+10\sqrt{3}}{2*2}=\frac{18+10\sqrt{3}}{4}
$