4x+3(x+6)=74/4x

Solution for 4x+3(x+6)=74/4x equation:

4x+3(x+6)=74/4x

We move all terms to the left:

4x+3(x+6)-(74/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x+3(x+6)-(+74/4x)=0

We multiply parentheses

4x+3x-(+74/4x)+18=0

We get rid of parentheses

4x+3x-74/4x+18=0

We multiply all the terms by the denominator


4x*4x+3x*4x+18*4x-74=0

Wy multiply elements

16x^2+12x^2+72x-74=0

We add all the numbers together, and all the variables

28x^2+72x-74=0

a = 28; b = 72; c = -74;
Δ = b2-4ac
Δ = 722-4·28·(-74)
Δ = 13472
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:

$\sqrt{\Delta}=\sqrt{13472}=\sqrt{16*842}=\sqrt{16}*\sqrt{842}=4\sqrt{842}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-4\sqrt{842}}{2*28}=\frac{-72-4\sqrt{842}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+4\sqrt{842}}{2*28}=\frac{-72+4\sqrt{842}}{56}
$