4y+-3=63/y=

Solution for 4y+-3=63/y= equation:

4y+-3=63/y=

We move all terms to the left:

4y+-3-(63/y)=0


Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

4y-(+63/y)-3+=0

We add all the numbers together, and all the variables

4y-(+63/y)=0

We get rid of parentheses

4y-63/y=0

We multiply all the terms by the denominator


4y*y-63=0

Wy multiply elements

4y^2-63=0

a = 4; b = 0; c = -63;
Δ = b2-4ac
Δ = 02-4·4·(-63)
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{7}}{2*4}=\frac{0-12\sqrt{7}}{8}
=-\frac{12\sqrt{7}}{8}
=-\frac{3\sqrt{7}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{7}}{2*4}=\frac{0+12\sqrt{7}}{8}
=\frac{12\sqrt{7}}{8}
=\frac{3\sqrt{7}}{2}
$