-8+3x=-16/25x

Solution for -8+3x=-16/25x equation:

-8+3x=-16/25x

We move all terms to the left:

-8+3x-(-16/25x)=0


Domain of the equation: 25x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

3x+16/25x-8=0

We multiply all the terms by the denominator


3x*25x-8*25x+16=0

Wy multiply elements

75x^2-200x+16=0

a = 75; b = -200; c = +16;
Δ = b2-4ac
Δ = -2002-4·75·16
Δ = 35200
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:

$\sqrt{\Delta}=\sqrt{35200}=\sqrt{1600*22}=\sqrt{1600}*\sqrt{22}=40\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-40\sqrt{22}}{2*75}=\frac{200-40\sqrt{22}}{150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+40\sqrt{22}}{2*75}=\frac{200+40\sqrt{22}}{150}
$