5y^2+2=10y+2

Solution for 5y^2+2=10y+2 equation:

5y^2+2=10y+2

We move all terms to the left:

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

We get rid of parentheses

5y^2-10y-2+2=0

We add all the numbers together, and all the variables

5y^2-10y=0

a = 5; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·5·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*5}=\frac{0}{10}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*5}=\frac{20}{10}
=2
$