5y(1/7)+(-15)=5y+30

Solution for 5y(1/7)+(-15)=5y+30 equation:

5y(1/7)+(-15)=5y+30

We move all terms to the left:

5y(1/7)+(-15)-(5y+30)=0

We add all the numbers together, and all the variables

5y(+1/7)-(5y+30)+(-15)=0

We add all the numbers together, and all the variables

5y(+1/7)-(5y+30)-15=0

We multiply parentheses

5y^2-(5y+30)-15=0

We get rid of parentheses

5y^2-5y-30-15=0

We add all the numbers together, and all the variables

5y^2-5y-45=0

a = 5; b = -5; c = -45;
Δ = b2-4ac
Δ = -52-4·5·(-45)
Δ = 925
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:

$\sqrt{\Delta}=\sqrt{925}=\sqrt{25*37}=\sqrt{25}*\sqrt{37}=5\sqrt{37}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{37}}{2*5}=\frac{5-5\sqrt{37}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{37}}{2*5}=\frac{5+5\sqrt{37}}{10}
$