4(-5-7n-)n=-223

Solution for 4(-5-7n-)n=-223 equation:

4(-5-7n-)n=-223

We move all terms to the left:

4(-5-7n-)n-(-223)=0

We add all the numbers together, and all the variables

4(-7n)n-(-223)=0

We add all the numbers together, and all the variables

4(-7n)n+223=0

We multiply parentheses

-28n^2+223=0

a = -28; b = 0; c = +223;
Δ = b2-4ac
Δ = 02-4·(-28)·223
Δ = 24976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24976}=\sqrt{16*1561}=\sqrt{16}*\sqrt{1561}=4\sqrt{1561}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{1561}}{2*-28}=\frac{0-4\sqrt{1561}}{-56}
=-\frac{4\sqrt{1561}}{-56}
=-\frac{\sqrt{1561}}{-14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{1561}}{2*-28}=\frac{0+4\sqrt{1561}}{-56}
=\frac{4\sqrt{1561}}{-56}
=\frac{\sqrt{1561}}{-14}
$