105n2=-224-308n

Solution for 105n2=-224-308n equation:

105n^2=-224-308n

We move all terms to the left:

105n^2-(-224-308n)=0

We add all the numbers together, and all the variables

105n^2-(-308n-224)=0

We get rid of parentheses

105n^2+308n+224=0

a = 105; b = 308; c = +224;
Δ = b2-4ac
Δ = 3082-4·105·224
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(308)-28}{2*105}=\frac{-336}{210}
=-1+3/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(308)+28}{2*105}=\frac{-280}{210}
=-1+1/3
$