2/25x+x=24

Solution for 2/25x+x=24 equation:

2/25x+x=24

We move all terms to the left:

2/25x+x-(24)=0


Domain of the equation: 25x!=0

x!=0/25

x!=0

x∈R


We add all the numbers together, and all the variables

x+2/25x-24=0

We multiply all the terms by the denominator


x*25x-24*25x+2=0

Wy multiply elements

25x^2-600x+2=0

a = 25; b = -600; c = +2;
Δ = b2-4ac
Δ = -6002-4·25·2
Δ = 359800
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:

$\sqrt{\Delta}=\sqrt{359800}=\sqrt{100*3598}=\sqrt{100}*\sqrt{3598}=10\sqrt{3598}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-10\sqrt{3598}}{2*25}=\frac{600-10\sqrt{3598}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+10\sqrt{3598}}{2*25}=\frac{600+10\sqrt{3598}}{50}
$