6-43m=-7m^2

Solution for 6-43m=-7m^2 equation:

6-43m=-7m^2

We move all terms to the left:

6-43m-(-7m^2)=0

We get rid of parentheses

7m^2-43m+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:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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