5a^2=48-a

Solution for 5a^2=48-a equation:

5a^2=48-a

We move all terms to the left:

5a^2-(48-a)=0

We add all the numbers together, and all the variables

5a^2-(-1a+48)=0

We get rid of parentheses

5a^2+1a-48=0

We add all the numbers together, and all the variables

5a^2+a-48=0

a = 5; b = 1; c = -48;
Δ = b2-4ac
Δ = 12-4·5·(-48)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-31}{2*5}=\frac{-32}{10}
=-3+1/5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+31}{2*5}=\frac{30}{10}
=3
$