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

Solution for 11y^2-19y-10=4y^2 equation:

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

We move all terms to the left:

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

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

We add all the numbers together, and all the variables

7y^2-19y-10=0

a = 7; b = -19; c = -10;
Δ = b2-4ac
Δ = -192-4·7·(-10)
Δ = 641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{641}}{2*7}=\frac{19-\sqrt{641}}{14}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{641}}{2*7}=\frac{19+\sqrt{641}}{14}
$