X+3/4x+1/4x=720

Solution for X+3/4x+1/4x=720 equation:

X+3/4X+1/4X=720

We move all terms to the left:

X+3/4X+1/4X-(720)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-720*4X+3+1=0

We add all the numbers together, and all the variables

X*4X-720*4X+4=0

Wy multiply elements

4X^2-2880X+4=0

a = 4; b = -2880; c = +4;
Δ = b2-4ac
Δ = -28802-4·4·4
Δ = 8294336
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:

$\sqrt{\Delta}=\sqrt{8294336}=\sqrt{23104*359}=\sqrt{23104}*\sqrt{359}=152\sqrt{359}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2880)-152\sqrt{359}}{2*4}=\frac{2880-152\sqrt{359}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2880)+152\sqrt{359}}{2*4}=\frac{2880+152\sqrt{359}}{8}
$