x+3/4x=77

Solution for x+3/4x=77 equation:

x+3/4x=77

We move all terms to the left:

x+3/4x-(77)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-77*4x+3=0

Wy multiply elements

4x^2-308x+3=0

a = 4; b = -308; c = +3;
Δ = b2-4ac
Δ = -3082-4·4·3
Δ = 94816
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:

$\sqrt{\Delta}=\sqrt{94816}=\sqrt{16*5926}=\sqrt{16}*\sqrt{5926}=4\sqrt{5926}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-308)-4\sqrt{5926}}{2*4}=\frac{308-4\sqrt{5926}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-308)+4\sqrt{5926}}{2*4}=\frac{308+4\sqrt{5926}}{8}
$