3/4x+2+x=50

Solution for 3/4x+2+x=50 equation:

3/4x+2+x=50

We move all terms to the left:

3/4x+2+x-(50)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/4x-48=0

We multiply all the terms by the denominator


x*4x-48*4x+3=0

Wy multiply elements

4x^2-192x+3=0

a = 4; b = -192; c = +3;
Δ = b2-4ac
Δ = -1922-4·4·3
Δ = 36816
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:

$\sqrt{\Delta}=\sqrt{36816}=\sqrt{16*2301}=\sqrt{16}*\sqrt{2301}=4\sqrt{2301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-4\sqrt{2301}}{2*4}=\frac{192-4\sqrt{2301}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+4\sqrt{2301}}{2*4}=\frac{192+4\sqrt{2301}}{8}
$