X=77-3/8x

Solution for X=77-3/8x equation:

X=77-3/8X

We move all terms to the left:

X-(77-3/8X)=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-(-3/8X+77)=0

We get rid of parentheses

X+3/8X-77=0

We multiply all the terms by the denominator


X*8X-77*8X+3=0

Wy multiply elements

8X^2-616X+3=0

a = 8; b = -616; c = +3;
Δ = b2-4ac
Δ = -6162-4·8·3
Δ = 379360
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:

$\sqrt{\Delta}=\sqrt{379360}=\sqrt{16*23710}=\sqrt{16}*\sqrt{23710}=4\sqrt{23710}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-616)-4\sqrt{23710}}{2*8}=\frac{616-4\sqrt{23710}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-616)+4\sqrt{23710}}{2*8}=\frac{616+4\sqrt{23710}}{16}
$