10a^2+a=2

Solution for 10a^2+a=2 equation:

10a^2+a=2

We move all terms to the left:

10a^2+a-(2)=0

a = 10; b = 1; c = -2;
Δ = b2-4ac
Δ = 12-4·10·(-2)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-9}{2*10}=\frac{-10}{20}
=-1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+9}{2*10}=\frac{8}{20}
=2/5
$