(1/4)x-(2/5)=7

Solution for (1/4)x-(2/5)=7 equation:

(1/4)x-(2/5)=7

We move all terms to the left:

(1/4)x-(2/5)-(7)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
(1/4)x-7-(2/5)=0

We add all the numbers together, and all the variables

(+1/4)x-7-(+2/5)=0

We multiply parentheses

x^2-7-(+2/5)=0

We get rid of parentheses

x^2-7-2/5=0

We multiply all the terms by the denominator


x^2*5-2-7*5=0

We add all the numbers together, and all the variables

x^2*5-37=0

Wy multiply elements

5x^2-37=0

a = 5; b = 0; c = -37;
Δ = b2-4ac
Δ = 02-4·5·(-37)
Δ = 740
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:

$\sqrt{\Delta}=\sqrt{740}=\sqrt{4*185}=\sqrt{4}*\sqrt{185}=2\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{185}}{2*5}=\frac{0-2\sqrt{185}}{10}
=-\frac{2\sqrt{185}}{10}
=-\frac{\sqrt{185}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{185}}{2*5}=\frac{0+2\sqrt{185}}{10}
=\frac{2\sqrt{185}}{10}
=\frac{\sqrt{185}}{5}
$