X+6/2=3/4x

Solution for X+6/2=3/4x equation:

X+6/2=3/4X

We move all terms to the left:

X+6/2-(3/4X)=0


Domain of the equation: 4X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+3/4X)+6/2=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

X-3/4X+3=0

We multiply all the terms by the denominator


X*4X+3*4X-3=0

Wy multiply elements

4X^2+12X-3=0

a = 4; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·4·(-3)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{3}}{2*4}=\frac{-12-8\sqrt{3}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{3}}{2*4}=\frac{-12+8\sqrt{3}}{8}
$