-7y(y+6)=-10y-45

Solution for -7y(y+6)=-10y-45 equation:

-7y(y+6)=-10y-45

We move all terms to the left:

-7y(y+6)-(-10y-45)=0

We multiply parentheses

-7y^2-42y-(-10y-45)=0

We get rid of parentheses

-7y^2-42y+10y+45=0

We add all the numbers together, and all the variables

-7y^2-32y+45=0

a = -7; b = -32; c = +45;
Δ = b2-4ac
Δ = -322-4·(-7)·45
Δ = 2284
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:

$\sqrt{\Delta}=\sqrt{2284}=\sqrt{4*571}=\sqrt{4}*\sqrt{571}=2\sqrt{571}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{571}}{2*-7}=\frac{32-2\sqrt{571}}{-14}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{571}}{2*-7}=\frac{32+2\sqrt{571}}{-14}
$