3-(1/5)x=-7

Solution for 3-(1/5)x=-7 equation:

3-(1/5)x=-7

We move all terms to the left:

3-(1/5)x-(-7)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+1/5)x+3-(-7)=0

We add all the numbers together, and all the variables

-(+1/5)x+10=0

We multiply parentheses

-x^2+10=0

We add all the numbers together, and all the variables

-1x^2+10=0

a = -1; b = 0; c = +10;
Δ = b2-4ac
Δ = 02-4·(-1)·10
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10}}{2*-1}=\frac{0-2\sqrt{10}}{-2}
=-\frac{2\sqrt{10}}{-2}
=-\frac{\sqrt{10}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10}}{2*-1}=\frac{0+2\sqrt{10}}{-2}
=\frac{2\sqrt{10}}{-2}
=\frac{\sqrt{10}}{-1}
$