3x+3/4x=36

Solution for 3x+3/4x=36 equation:

3x+3/4x=36

We move all terms to the left:

3x+3/4x-(36)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


3x*4x-36*4x+3=0

Wy multiply elements

12x^2-144x+3=0

a = 12; b = -144; c = +3;
Δ = b2-4ac
Δ = -1442-4·12·3
Δ = 20592
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:

$\sqrt{\Delta}=\sqrt{20592}=\sqrt{144*143}=\sqrt{144}*\sqrt{143}=12\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-12\sqrt{143}}{2*12}=\frac{144-12\sqrt{143}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+12\sqrt{143}}{2*12}=\frac{144+12\sqrt{143}}{24}
$