y(y+10)=5/12

Solution for y(y+10)=5/12 equation:

y(y+10)=5/12

We move all terms to the left:

y(y+10)-(5/12)=0

We add all the numbers together, and all the variables

y(y+10)-(+5/12)=0

We multiply parentheses

y^2+10y-(+5/12)=0

We get rid of parentheses

y^2+10y-5/12=0

We multiply all the terms by the denominator


y^2*12+10y*12-5=0

Wy multiply elements

12y^2+120y-5=0

a = 12; b = 120; c = -5;
Δ = b2-4ac
Δ = 1202-4·12·(-5)
Δ = 14640
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:

$\sqrt{\Delta}=\sqrt{14640}=\sqrt{16*915}=\sqrt{16}*\sqrt{915}=4\sqrt{915}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-4\sqrt{915}}{2*12}=\frac{-120-4\sqrt{915}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+4\sqrt{915}}{2*12}=\frac{-120+4\sqrt{915}}{24}
$