7n+5=19(n2)

Solution for 7n+5=19(n2) equation:

7n+5=19(n2)

We move all terms to the left:

7n+5-(19(n2))=0

determiningTheFunctionDomain
7n-19n2+5=0

We add all the numbers together, and all the variables

-19n^2+7n+5=0

a = -19; b = 7; c = +5;
Δ = b2-4ac
Δ = 72-4·(-19)·5
Δ = 429
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{429}}{2*-19}=\frac{-7-\sqrt{429}}{-38}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{429}}{2*-19}=\frac{-7+\sqrt{429}}{-38}
$