3/8y+45=6y

Solution for 3/8y+45=6y equation:

3/8y+45=6y

We move all terms to the left:

3/8y+45-(6y)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R


We add all the numbers together, and all the variables

-6y+3/8y+45=0

We multiply all the terms by the denominator


-6y*8y+45*8y+3=0

Wy multiply elements

-48y^2+360y+3=0

a = -48; b = 360; c = +3;
Δ = b2-4ac
Δ = 3602-4·(-48)·3
Δ = 130176
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:

$\sqrt{\Delta}=\sqrt{130176}=\sqrt{576*226}=\sqrt{576}*\sqrt{226}=24\sqrt{226}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-24\sqrt{226}}{2*-48}=\frac{-360-24\sqrt{226}}{-96}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+24\sqrt{226}}{2*-48}=\frac{-360+24\sqrt{226}}{-96}
$