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+10+7a)=0

We get rid of parentheses

-6a^2+3a-7a-10+21=0

We add all the numbers together, and all the variables

-6a^2-4a+11=0

a = -6; b = -4; c = +11;
Δ = b2-4ac
Δ = -42-4·(-6)·11
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{70}}{2*-6}=\frac{4-2\sqrt{70}}{-12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{70}}{2*-6}=\frac{4+2\sqrt{70}}{-12}
$