88=x+4/7x

Solution for 88=x+4/7x equation:

88=x+4/7x

We move all terms to the left:

88-(x+4/7x)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x+4/7x)+88=0

We get rid of parentheses

-x-4/7x+88=0

We multiply all the terms by the denominator


-x*7x+88*7x-4=0

Wy multiply elements

-7x^2+616x-4=0

a = -7; b = 616; c = -4;
Δ = b2-4ac
Δ = 6162-4·(-7)·(-4)
Δ = 379344
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:

$\sqrt{\Delta}=\sqrt{379344}=\sqrt{16*23709}=\sqrt{16}*\sqrt{23709}=4\sqrt{23709}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(616)-4\sqrt{23709}}{2*-7}=\frac{-616-4\sqrt{23709}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(616)+4\sqrt{23709}}{2*-7}=\frac{-616+4\sqrt{23709}}{-14}
$