45=125-5/3y-y

Solution for 45=125-5/3y-y equation:

45=125-5/3y-y

We move all terms to the left:

45-(125-5/3y-y)=0


Domain of the equation: 3y-y)!=0

y∈R


We add all the numbers together, and all the variables

-(-1y-5/3y+125)+45=0

We get rid of parentheses

1y+5/3y-125+45=0

We multiply all the terms by the denominator


1y*3y-125*3y+45*3y+5=0

Wy multiply elements

3y^2-375y+135y+5=0

We add all the numbers together, and all the variables

3y^2-240y+5=0

a = 3; b = -240; c = +5;
Δ = b2-4ac
Δ = -2402-4·3·5
Δ = 57540
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:

$\sqrt{\Delta}=\sqrt{57540}=\sqrt{4*14385}=\sqrt{4}*\sqrt{14385}=2\sqrt{14385}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-2\sqrt{14385}}{2*3}=\frac{240-2\sqrt{14385}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+2\sqrt{14385}}{2*3}=\frac{240+2\sqrt{14385}}{6}
$