3x+8=88/x

Solution for 3x+8=88/x equation:

3x+8=88/x

We move all terms to the left:

3x+8-(88/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+88/x)+8=0

We get rid of parentheses

3x-88/x+8=0

We multiply all the terms by the denominator


3x*x+8*x-88=0

We add all the numbers together, and all the variables

8x+3x*x-88=0

Wy multiply elements

3x^2+8x-88=0

a = 3; b = 8; c = -88;
Δ = b2-4ac
Δ = 82-4·3·(-88)
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{70}}{2*3}=\frac{-8-4\sqrt{70}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{70}}{2*3}=\frac{-8+4\sqrt{70}}{6}
$