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

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

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

We move all terms to the left:

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

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

We add all the numbers together, and all the variables

-5y^2+23y-3=0

a = -5; b = 23; c = -3;
Δ = b2-4ac
Δ = 232-4·(-5)·(-3)
Δ = 469
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{-(23)-\sqrt{469}}{2*-5}=\frac{-23-\sqrt{469}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{469}}{2*-5}=\frac{-23+\sqrt{469}}{-10}
$