3/4x+14-2x=49

Solution for 3/4x+14-2x=49 equation:

3/4x+14-2x=49

We move all terms to the left:

3/4x+14-2x-(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

-2x+3/4x-35=0

We multiply all the terms by the denominator


-2x*4x-35*4x+3=0

Wy multiply elements

-8x^2-140x+3=0

a = -8; b = -140; c = +3;
Δ = b2-4ac
Δ = -1402-4·(-8)·3
Δ = 19696
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:

$\sqrt{\Delta}=\sqrt{19696}=\sqrt{16*1231}=\sqrt{16}*\sqrt{1231}=4\sqrt{1231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-4\sqrt{1231}}{2*-8}=\frac{140-4\sqrt{1231}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+4\sqrt{1231}}{2*-8}=\frac{140+4\sqrt{1231}}{-16}
$