11y2-19y-10=-4y2

Solution for 11y2-19y-10=-4y2 equation:

11y^2-19y-10=-4y^2

We move all terms to the left:

11y^2-19y-10-(-4y^2)=0

We get rid of parentheses

11y^2+4y^2-19y-10=0

We add all the numbers together, and all the variables

15y^2-19y-10=0

a = 15; b = -19; c = -10;
Δ = b2-4ac
Δ = -192-4·15·(-10)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-31}{2*15}=\frac{-12}{30}
=-2/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+31}{2*15}=\frac{50}{30}
=1+2/3
$