5a^2=10-9a

Solution for 5a^2=10-9a equation:

5a^2=10-9a

We move all terms to the left:

5a^2-(10-9a)=0

We add all the numbers together, and all the variables

5a^2-(-9a+10)=0

We get rid of parentheses

5a^2+9a-10=0

a = 5; b = 9; c = -10;
Δ = b2-4ac
Δ = 92-4·5·(-10)
Δ = 281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{281}}{2*5}=\frac{-9-\sqrt{281}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{281}}{2*5}=\frac{-9+\sqrt{281}}{10}
$