x-19/24x=40

Solution for x-19/24x=40 equation:

x-19/24x=40

We move all terms to the left:

x-19/24x-(40)=0


Domain of the equation: 24x!=0

x!=0/24

x!=0

x∈R


We multiply all the terms by the denominator


x*24x-40*24x-19=0

Wy multiply elements

24x^2-960x-19=0

a = 24; b = -960; c = -19;
Δ = b2-4ac
Δ = -9602-4·24·(-19)
Δ = 923424
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:

$\sqrt{\Delta}=\sqrt{923424}=\sqrt{16*57714}=\sqrt{16}*\sqrt{57714}=4\sqrt{57714}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-960)-4\sqrt{57714}}{2*24}=\frac{960-4\sqrt{57714}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-960)+4\sqrt{57714}}{2*24}=\frac{960+4\sqrt{57714}}{48}
$