7x=12+3/4x

Solution for 7x=12+3/4x equation:

7x=12+3/4x

We move all terms to the left:

7x-(12+3/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7x-(3/4x+12)=0

We get rid of parentheses

7x-3/4x-12=0

We multiply all the terms by the denominator


7x*4x-12*4x-3=0

Wy multiply elements

28x^2-48x-3=0

a = 28; b = -48; c = -3;
Δ = b2-4ac
Δ = -482-4·28·(-3)
Δ = 2640
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:

$\sqrt{\Delta}=\sqrt{2640}=\sqrt{16*165}=\sqrt{16}*\sqrt{165}=4\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{165}}{2*28}=\frac{48-4\sqrt{165}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{165}}{2*28}=\frac{48+4\sqrt{165}}{56}
$