(2/5)y-(3/5)y+5=-7

Solution for (2/5)y-(3/5)y+5=-7 equation:

(2/5)y-(3/5)y+5=-7

We move all terms to the left:

(2/5)y-(3/5)y+5-(-7)=0


Domain of the equation: 5)y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+2/5)y-(+3/5)y+5-(-7)=0

We add all the numbers together, and all the variables

(+2/5)y-(+3/5)y+12=0

We multiply parentheses

2y^2-3y^2+12=0

We add all the numbers together, and all the variables

-1y^2+12=0

a = -1; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-1)·12
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*-1}=\frac{0-4\sqrt{3}}{-2}
=-\frac{4\sqrt{3}}{-2}
=-\frac{2\sqrt{3}}{-1}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*-1}=\frac{0+4\sqrt{3}}{-2}
=\frac{4\sqrt{3}}{-2}
=\frac{2\sqrt{3}}{-1}
$