3/4x-4=3x+14

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

3/4x-4=3x+14

We move all terms to the left:

3/4x-4-(3x+14)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-3x-14-4=0

We multiply all the terms by the denominator


-3x*4x-14*4x-4*4x+3=0

Wy multiply elements

-12x^2-56x-16x+3=0

We add all the numbers together, and all the variables

-12x^2-72x+3=0

a = -12; b = -72; c = +3;
Δ = b2-4ac
Δ = -722-4·(-12)·3
Δ = 5328
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:

$\sqrt{\Delta}=\sqrt{5328}=\sqrt{144*37}=\sqrt{144}*\sqrt{37}=12\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12\sqrt{37}}{2*-12}=\frac{72-12\sqrt{37}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12\sqrt{37}}{2*-12}=\frac{72+12\sqrt{37}}{-24}
$