2x+3/4x+1=100

Solution for 2x+3/4x+1=100 equation:

2x+3/4x+1=100

We move all terms to the left:

2x+3/4x+1-(100)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2x+3/4x-99=0

We multiply all the terms by the denominator


2x*4x-99*4x+3=0

Wy multiply elements

8x^2-396x+3=0

a = 8; b = -396; c = +3;
Δ = b2-4ac
Δ = -3962-4·8·3
Δ = 156720
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:

$\sqrt{\Delta}=\sqrt{156720}=\sqrt{16*9795}=\sqrt{16}*\sqrt{9795}=4\sqrt{9795}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-396)-4\sqrt{9795}}{2*8}=\frac{396-4\sqrt{9795}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-396)+4\sqrt{9795}}{2*8}=\frac{396+4\sqrt{9795}}{16}
$