X+(7/8x)=600

Solution for X+(7/8x)=600 equation:

X+(7/8X)=600

We move all terms to the left:

X+(7/8X)-(600)=0


Domain of the equation: 8X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X+(+7/8X)-600=0

We get rid of parentheses

X+7/8X-600=0

We multiply all the terms by the denominator


X*8X-600*8X+7=0

Wy multiply elements

8X^2-4800X+7=0

a = 8; b = -4800; c = +7;
Δ = b2-4ac
Δ = -48002-4·8·7
Δ = 23039776
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:

$\sqrt{\Delta}=\sqrt{23039776}=\sqrt{16*1439986}=\sqrt{16}*\sqrt{1439986}=4\sqrt{1439986}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4800)-4\sqrt{1439986}}{2*8}=\frac{4800-4\sqrt{1439986}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4800)+4\sqrt{1439986}}{2*8}=\frac{4800+4\sqrt{1439986}}{16}
$