0.7n(n+19)=-2.8(n-1)

Solution for 0.7n(n+19)=-2.8(n-1) equation:

0.7n(n+19)=-2.8(n-1)

We move all terms to the left:

0.7n(n+19)-(-2.8(n-1))=0

We multiply parentheses

0n^2+0n-(-2.8(n-1))=0


We calculate terms in parentheses: -(-2.8(n-1)), so:

-2.8(n-1)

We multiply parentheses

-2.8n+2.8

Back to the equation:

-(-2.8n+2.8)


We add all the numbers together, and all the variables

n^2+n-(-2.8n+2.8)=0

We get rid of parentheses

n^2+n+2.8n-2.8=0

We add all the numbers together, and all the variables

n^2+3.8n-2.8=0

a = 1; b = 3.8; c = -2.8;
Δ = b2-4ac
Δ = 3.82-4·1·(-2.8)
Δ = 25.64
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{-(3.8)-\sqrt{25.64}}{2*1}=\frac{-3.8-\sqrt{25.64}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3.8)+\sqrt{25.64}}{2*1}=\frac{-3.8+\sqrt{25.64}}{2}
$