115=5x+1/4x

Solution for 115=5x+1/4x equation:

115=5x+1/4x

We move all terms to the left:

115-(5x+1/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+5x+1/4x)+115=0

We get rid of parentheses

-5x-1/4x+115=0

We multiply all the terms by the denominator


-5x*4x+115*4x-1=0

Wy multiply elements

-20x^2+460x-1=0

a = -20; b = 460; c = -1;
Δ = b2-4ac
Δ = 4602-4·(-20)·(-1)
Δ = 211520
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:

$\sqrt{\Delta}=\sqrt{211520}=\sqrt{64*3305}=\sqrt{64}*\sqrt{3305}=8\sqrt{3305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(460)-8\sqrt{3305}}{2*-20}=\frac{-460-8\sqrt{3305}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(460)+8\sqrt{3305}}{2*-20}=\frac{-460+8\sqrt{3305}}{-40}
$