0,5y(y+1)=6/7

Solution for 0,5y(y+1)=6/7 equation:

0.5y(y+1)=6/7

We move all terms to the left:

0.5y(y+1)-(6/7)=0

We add all the numbers together, and all the variables

0.5y(y+1)-(+6/7)=0

We multiply parentheses

0y^2+0y-(+6/7)=0

We get rid of parentheses

0y^2+0y-6/7=0

We multiply all the terms by the denominator


0y^2*7+0y*7-6=0

Wy multiply elements

0y^2+0y-6=0

We add all the numbers together, and all the variables

y^2+y-6=0

a = 1; b = 1; c = -6;
Δ = b2-4ac
Δ = 12-4·1·(-6)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5}{2*1}=\frac{-6}{2}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*1}=\frac{4}{2}
=2
$