24/1+x=10/x-0.75

Solution for 24/1+x=10/x-0.75 equation:

24/1+x=10/x-0.75

We move all terms to the left:

24/1+x-(10/x-0.75)=0


Domain of the equation: x-0.75)!=0

x∈R


We add all the numbers together, and all the variables

x-(10/x-0.75)=0

We get rid of parentheses

x-10/x+0.75=0

We multiply all the terms by the denominator


x*x+(0.75)*x-10=0

We multiply parentheses

x*x+0.75x-10=0

Wy multiply elements

x^2+0.75x-10=0

a = 1; b = 0.75; c = -10;
Δ = b2-4ac
Δ = 0.752-4·1·(-10)
Δ = 40.5625
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{-(0.75)-\sqrt{40.5625}}{2*1}=\frac{-0.75-\sqrt{40.5625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.75)+\sqrt{40.5625}}{2*1}=\frac{-0.75+\sqrt{40.5625}}{2}
$