3/4x+x=42

Solution for 3/4x+x=42 equation:

3/4x+x=42

We move all terms to the left:

3/4x+x-(42)=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-42=0

We multiply all the terms by the denominator


x*4x-42*4x+3=0

Wy multiply elements

4x^2-168x+3=0

a = 4; b = -168; c = +3;
Δ = b2-4ac
Δ = -1682-4·4·3
Δ = 28176
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:

$\sqrt{\Delta}=\sqrt{28176}=\sqrt{16*1761}=\sqrt{16}*\sqrt{1761}=4\sqrt{1761}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-4\sqrt{1761}}{2*4}=\frac{168-4\sqrt{1761}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+4\sqrt{1761}}{2*4}=\frac{168+4\sqrt{1761}}{8}
$