X=3x/4x+7

Solution for X=3x/4x+7 equation:

X=3X/4X+7

We move all terms to the left:

X-(3X/4X+7)=0


Domain of the equation: 4X+7)!=0

X∈R


We get rid of parentheses

X-3X/4X-7=0

We multiply all the terms by the denominator


X*4X-3X-7*4X=0

We add all the numbers together, and all the variables

-3X+X*4X-7*4X=0

Wy multiply elements

4X^2-3X-28X=0

We add all the numbers together, and all the variables

4X^2-31X=0

a = 4; b = -31; c = 0;
Δ = b2-4ac
Δ = -312-4·4·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-31}{2*4}=\frac{0}{8}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+31}{2*4}=\frac{62}{8}
=7+3/4
$