21+3a=6a^2=10+7a

Solution for 21+3a=6a^2=10+7a equation:

21+3a=6a^2=10+7a

We move all terms to the left:

21+3a-(6a^2)=0

determiningTheFunctionDomain
-6a^2+3a+21=0

a = -6; b = 3; c = +21;
Δ = b2-4ac
Δ = 32-4·(-6)·21
Δ = 513
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{57}}{2*-6}=\frac{-3-3\sqrt{57}}{-12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{57}}{2*-6}=\frac{-3+3\sqrt{57}}{-12}
$