x-(2/5x)+21=40

Solution for x-(2/5x)+21=40 equation:

x-(2/5x)+21=40

We move all terms to the left:

x-(2/5x)+21-(40)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+2/5x)+21-40=0

We add all the numbers together, and all the variables

x-(+2/5x)-19=0

We get rid of parentheses

x-2/5x-19=0

We multiply all the terms by the denominator


x*5x-19*5x-2=0

Wy multiply elements

5x^2-95x-2=0

a = 5; b = -95; c = -2;
Δ = b2-4ac
Δ = -952-4·5·(-2)
Δ = 9065
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:

$\sqrt{\Delta}=\sqrt{9065}=\sqrt{49*185}=\sqrt{49}*\sqrt{185}=7\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-95)-7\sqrt{185}}{2*5}=\frac{95-7\sqrt{185}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-95)+7\sqrt{185}}{2*5}=\frac{95+7\sqrt{185}}{10}
$