6y(-5y-10)=(y+11)(y+1)-y2+31

Solution for 6y(-5y-10)=(y+11)(y+1)-y2+31 equation:

6y(-5y-10)=(y+11)(y+1)-y2+31

We move all terms to the left:

6y(-5y-10)-((y+11)(y+1)-y2+31)=0

We multiply parentheses

-30y^2-60y-((y+11)(y+1)-y2+31)=0

We multiply parentheses ..

-30y^2-((+y^2+y+11y+11)-y2+31)-60y=0


We calculate terms in parentheses: -((+y^2+y+11y+11)-y2+31), so:

(+y^2+y+11y+11)-y2+31

We add all the numbers together, and all the variables

-1y^2+(+y^2+y+11y+11)+31

We get rid of parentheses

-1y^2+y^2+y+11y+11+31

We add all the numbers together, and all the variables

12y+42

Back to the equation:

-(12y+42)


We add all the numbers together, and all the variables

-30y^2-60y-(12y+42)=0

We get rid of parentheses

-30y^2-60y-12y-42=0

We add all the numbers together, and all the variables

-30y^2-72y-42=0

a = -30; b = -72; c = -42;
Δ = b2-4ac
Δ = -722-4·(-30)·(-42)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12}{2*-30}=\frac{60}{-60}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12}{2*-30}=\frac{84}{-60}
=-1+2/5
$