(3/8)y=23/4

Solution for (3/8)y=23/4 equation:

(3/8)y=23/4

We move all terms to the left:

(3/8)y-(23/4)=0


Domain of the equation: 8)y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+3/8)y-(+23/4)=0

We multiply parentheses

3y^2-(+23/4)=0

We get rid of parentheses

3y^2-23/4=0

We multiply all the terms by the denominator


3y^2*4-23=0

Wy multiply elements

12y^2-23=0

a = 12; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·12·(-23)
Δ = 1104
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:

$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{69}}{2*12}=\frac{0-4\sqrt{69}}{24}
=-\frac{4\sqrt{69}}{24}
=-\frac{\sqrt{69}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{69}}{2*12}=\frac{0+4\sqrt{69}}{24}
=\frac{4\sqrt{69}}{24}
=\frac{\sqrt{69}}{6}
$