3x=100-3/4x

Solution for 3x=100-3/4x equation:

3x=100-3/4x

We move all terms to the left:

3x-(100-3/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(-3/4x+100)=0

We get rid of parentheses

3x+3/4x-100=0

We multiply all the terms by the denominator


3x*4x-100*4x+3=0

Wy multiply elements

12x^2-400x+3=0

a = 12; b = -400; c = +3;
Δ = b2-4ac
Δ = -4002-4·12·3
Δ = 159856
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:

$\sqrt{\Delta}=\sqrt{159856}=\sqrt{16*9991}=\sqrt{16}*\sqrt{9991}=4\sqrt{9991}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-4\sqrt{9991}}{2*12}=\frac{400-4\sqrt{9991}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+4\sqrt{9991}}{2*12}=\frac{400+4\sqrt{9991}}{24}
$