10y^2=13y-4

Solution for 10y^2=13y-4 equation:

10y^2=13y-4

We move all terms to the left:

10y^2-(13y-4)=0

We get rid of parentheses

10y^2-13y+4=0

a = 10; b = -13; c = +4;
Δ = b2-4ac
Δ = -132-4·10·4
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-3}{2*10}=\frac{10}{20}
=1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3}{2*10}=\frac{16}{20}
=4/5
$