2x+1/4x+3x=90

Solution for 2x+1/4x+3x=90 equation:

2x+1/4x+3x=90

We move all terms to the left:

2x+1/4x+3x-(90)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

5x+1/4x-90=0

We multiply all the terms by the denominator


5x*4x-90*4x+1=0

Wy multiply elements

20x^2-360x+1=0

a = 20; b = -360; c = +1;
Δ = b2-4ac
Δ = -3602-4·20·1
Δ = 129520
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:

$\sqrt{\Delta}=\sqrt{129520}=\sqrt{16*8095}=\sqrt{16}*\sqrt{8095}=4\sqrt{8095}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-4\sqrt{8095}}{2*20}=\frac{360-4\sqrt{8095}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+4\sqrt{8095}}{2*20}=\frac{360+4\sqrt{8095}}{40}
$