3/4x+x=49

Solution for 3/4x+x=49 equation:

3/4x+x=49

We move all terms to the left:

3/4x+x-(49)=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-49=0

We multiply all the terms by the denominator


x*4x-49*4x+3=0

Wy multiply elements

4x^2-196x+3=0

a = 4; b = -196; c = +3;
Δ = b2-4ac
Δ = -1962-4·4·3
Δ = 38368
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:

$\sqrt{\Delta}=\sqrt{38368}=\sqrt{16*2398}=\sqrt{16}*\sqrt{2398}=4\sqrt{2398}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-196)-4\sqrt{2398}}{2*4}=\frac{196-4\sqrt{2398}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-196)+4\sqrt{2398}}{2*4}=\frac{196+4\sqrt{2398}}{8}
$