X=3x/2x-7

Solution for X=3x/2x-7 equation:

X=3X/2X-7

We move all terms to the left:

X-(3X/2X-7)=0


Domain of the equation: 2X-7)!=0

X∈R


We get rid of parentheses

X-3X/2X+7=0

We multiply all the terms by the denominator


X*2X-3X+7*2X=0

We add all the numbers together, and all the variables

-3X+X*2X+7*2X=0

Wy multiply elements

2X^2-3X+14X=0

We add all the numbers together, and all the variables

2X^2+11X=0

a = 2; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·2·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*2}=\frac{-22}{4}
=-5+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*2}=\frac{0}{4}
=0
$