25/4x=15x+80

Solution for 25/4x=15x+80 equation:

25/4x=15x+80

We move all terms to the left:

25/4x-(15x+80)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

25/4x-15x-80=0

We multiply all the terms by the denominator


-15x*4x-80*4x+25=0

Wy multiply elements

-60x^2-320x+25=0

a = -60; b = -320; c = +25;
Δ = b2-4ac
Δ = -3202-4·(-60)·25
Δ = 108400
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:

$\sqrt{\Delta}=\sqrt{108400}=\sqrt{400*271}=\sqrt{400}*\sqrt{271}=20\sqrt{271}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-20\sqrt{271}}{2*-60}=\frac{320-20\sqrt{271}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+20\sqrt{271}}{2*-60}=\frac{320+20\sqrt{271}}{-120}
$