13y^2+10y-3=5y^2

Solution for 13y^2+10y-3=5y^2 equation:

13y^2+10y-3=5y^2

We move all terms to the left:

13y^2+10y-3-(5y^2)=0

determiningTheFunctionDomain
13y^2-5y^2+10y-3=0

We add all the numbers together, and all the variables

8y^2+10y-3=0

a = 8; b = 10; c = -3;
Δ = b2-4ac
Δ = 102-4·8·(-3)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*8}=\frac{-24}{16}
=-1+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*8}=\frac{4}{16}
=1/4
$