42a=-432-a2

Solution for 42a=-432-a2 equation:

42a=-432-a2

We move all terms to the left:

42a-(-432-a2)=0

We add all the numbers together, and all the variables

-(-1a^2-432)+42a=0

We get rid of parentheses

1a^2+42a+432=0

We add all the numbers together, and all the variables

a^2+42a+432=0

a = 1; b = 42; c = +432;
Δ = b2-4ac
Δ = 422-4·1·432
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6}{2*1}=\frac{-48}{2}
=-24
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6}{2*1}=\frac{-36}{2}
=-18
$