24/10x-2x=3/1

Solution for 24/10x-2x=3/1 equation:

24/10x-2x=3/1

We move all terms to the left:

24/10x-2x-(3/1)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

24/10x-2x-0=0

We add all the numbers together, and all the variables

-2x+24/10x=0

We multiply all the terms by the denominator


-2x*10x+24=0

Wy multiply elements

-20x^2+24=0

a = -20; b = 0; c = +24;
Δ = b2-4ac
Δ = 02-4·(-20)·24
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{30}}{2*-20}=\frac{0-8\sqrt{30}}{-40}
=-\frac{8\sqrt{30}}{-40}
=-\frac{\sqrt{30}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{30}}{2*-20}=\frac{0+8\sqrt{30}}{-40}
=\frac{8\sqrt{30}}{-40}
=\frac{\sqrt{30}}{-5}
$