8x-5/x=5x-12.5

Solution for 8x-5/x=5x-12.5 equation:

8x-5/x=5x-12.5

We move all terms to the left:

8x-5/x-(5x-12.5)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

8x-5/x-5x+12.5=0

We multiply all the terms by the denominator


8x*x-5x*x+(12.5)*x-5=0

We multiply parentheses

8x*x-5x*x+12.5x-5=0

Wy multiply elements

8x^2-5x^2+12.5x-5=0

We add all the numbers together, and all the variables

3x^2+12.5x-5=0

a = 3; b = 12.5; c = -5;
Δ = b2-4ac
Δ = 12.52-4·3·(-5)
Δ = 216.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12.5)-\sqrt{216.25}}{2*3}=\frac{-12.5-\sqrt{216.25}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12.5)+\sqrt{216.25}}{2*3}=\frac{-12.5+\sqrt{216.25}}{6}
$