x+3/8x=77

Solution for x+3/8x=77 equation:

x+3/8x=77

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


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}
$