3/4*x+2+x+2=50

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

3/4x+2+x+2=50

We move all terms to the left:

3/4x+2+x+2-(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-46=0

We multiply all the terms by the denominator


x*4x-46*4x+3=0

Wy multiply elements

4x^2-184x+3=0

a = 4; b = -184; c = +3;
Δ = b2-4ac
Δ = -1842-4·4·3
Δ = 33808
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:

$\sqrt{\Delta}=\sqrt{33808}=\sqrt{16*2113}=\sqrt{16}*\sqrt{2113}=4\sqrt{2113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-184)-4\sqrt{2113}}{2*4}=\frac{184-4\sqrt{2113}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-184)+4\sqrt{2113}}{2*4}=\frac{184+4\sqrt{2113}}{8}
$