24/x+10=3x-4

Solution for 24/x+10=3x-4 equation:

24/x+10=3x-4

We move all terms to the left:

24/x+10-(3x-4)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

24/x-3x+4+10=0

We multiply all the terms by the denominator


-3x*x+4*x+10*x+24=0

We add all the numbers together, and all the variables

14x-3x*x+24=0

Wy multiply elements

-3x^2+14x+24=0

a = -3; b = 14; c = +24;
Δ = b2-4ac
Δ = 142-4·(-3)·24
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-22}{2*-3}=\frac{-36}{-6}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+22}{2*-3}=\frac{8}{-6}
=-1+1/3
$