50/4x=x+15

Solution for 50/4x=x+15 equation:

50/4x=x+15

We move all terms to the left:

50/4x-(x+15)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

50/4x-x-15=0

We multiply all the terms by the denominator


-x*4x-15*4x+50=0

Wy multiply elements

-4x^2-60x+50=0

a = -4; b = -60; c = +50;
Δ = b2-4ac
Δ = -602-4·(-4)·50
Δ = 4400
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:

$\sqrt{\Delta}=\sqrt{4400}=\sqrt{400*11}=\sqrt{400}*\sqrt{11}=20\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-20\sqrt{11}}{2*-4}=\frac{60-20\sqrt{11}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+20\sqrt{11}}{2*-4}=\frac{60+20\sqrt{11}}{-8}
$