3a^2=48-7a

Solution for 3a^2=48-7a equation:

3a^2=48-7a

We move all terms to the left:

3a^2-(48-7a)=0

We add all the numbers together, and all the variables

3a^2-(-7a+48)=0

We get rid of parentheses

3a^2+7a-48=0

a = 3; b = 7; c = -48;
Δ = b2-4ac
Δ = 72-4·3·(-48)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-25}{2*3}=\frac{-32}{6}
=-5+1/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+25}{2*3}=\frac{18}{6}
=3
$