25/x+50-75=5x

Solution for 25/x+50-75=5x equation:

25/x+50-75=5x

We move all terms to the left:

25/x+50-75-(5x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-5x+25/x-25=0

We multiply all the terms by the denominator


-5x*x-25*x+25=0

We add all the numbers together, and all the variables

-25x-5x*x+25=0

Wy multiply elements

-5x^2-25x+25=0

a = -5; b = -25; c = +25;
Δ = b2-4ac
Δ = -252-4·(-5)·25
Δ = 1125
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:

$\sqrt{\Delta}=\sqrt{1125}=\sqrt{225*5}=\sqrt{225}*\sqrt{5}=15\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-15\sqrt{5}}{2*-5}=\frac{25-15\sqrt{5}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+15\sqrt{5}}{2*-5}=\frac{25+15\sqrt{5}}{-10}
$