7a^2+6=-43a

Solution for 7a^2+6=-43a equation:

7a^2+6=-43a

We move all terms to the left:

7a^2+6-(-43a)=0

We get rid of parentheses

7a^2+43a+6=0

a = 7; b = 43; c = +6;
Δ = b2-4ac
Δ = 432-4·7·6
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-41}{2*7}=\frac{-84}{14}
=-6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+41}{2*7}=\frac{-2}{14}
=-1/7
$