3(127/3)-15+2(127/3)(y)(y)=180

Solution for 3(127/3)-15+2(127/3)(y)(y)=180 equation:

3(127/3)-15+2(127/3)(y)(y)=180

We move all terms to the left:

3(127/3)-15+2(127/3)(y)(y)-(180)=0


Domain of the equation: 3)yy!=0

y!=0/1

y!=0

y∈R


determiningTheFunctionDomain
2(127/3)yy-15-180+3(127/3)=0

We add all the numbers together, and all the variables

2(+127/3)yy-15-180+3(+127/3)=0

We add all the numbers together, and all the variables

2(+127/3)yy-194=0

We multiply parentheses

254y^2-194=0

a = 254; b = 0; c = -194;
Δ = b2-4ac
Δ = 02-4·254·(-194)
Δ = 197104
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:

$\sqrt{\Delta}=\sqrt{197104}=\sqrt{16*12319}=\sqrt{16}*\sqrt{12319}=4\sqrt{12319}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{12319}}{2*254}=\frac{0-4\sqrt{12319}}{508}
=-\frac{4\sqrt{12319}}{508}
=-\frac{\sqrt{12319}}{127}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{12319}}{2*254}=\frac{0+4\sqrt{12319}}{508}
=\frac{4\sqrt{12319}}{508}
=\frac{\sqrt{12319}}{127}
$