3x+2/2+4x-5/43x-8/8=16

Solution for 3x+2/2+4x-5/43x-8/8=16 equation:

3x+2/2+4x-5/43x-8/8=16

We move all terms to the left:

3x+2/2+4x-5/43x-8/8-(16)=0


Domain of the equation: 43x!=0

x!=0/43

x!=0

x∈R


determiningTheFunctionDomain
3x+4x-5/43x-16+2/2-8/8=0

We add all the numbers together, and all the variables

7x-5/43x-16=0

We multiply all the terms by the denominator


7x*43x-16*43x-5=0

Wy multiply elements

301x^2-688x-5=0

a = 301; b = -688; c = -5;
Δ = b2-4ac
Δ = -6882-4·301·(-5)
Δ = 479364
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:

$\sqrt{\Delta}=\sqrt{479364}=\sqrt{4*119841}=\sqrt{4}*\sqrt{119841}=2\sqrt{119841}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-688)-2\sqrt{119841}}{2*301}=\frac{688-2\sqrt{119841}}{602}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-688)+2\sqrt{119841}}{2*301}=\frac{688+2\sqrt{119841}}{602}
$