-2k-19=-7k(-2+5k)

Solution for -2k-19=-7k(-2+5k) equation:

-2k-19=-7k(-2+5k)

We move all terms to the left:

-2k-19-(-7k(-2+5k))=0

We add all the numbers together, and all the variables

-2k-(-7k(5k-2))-19=0


We calculate terms in parentheses: -(-7k(5k-2)), so:

-7k(5k-2)

We multiply parentheses

-35k^2+14k

Back to the equation:

-(-35k^2+14k)


We get rid of parentheses

35k^2-14k-2k-19=0

We add all the numbers together, and all the variables

35k^2-16k-19=0

a = 35; b = -16; c = -19;
Δ = b2-4ac
Δ = -162-4·35·(-19)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-54}{2*35}=\frac{-38}{70}
=-19/35
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+54}{2*35}=\frac{70}{70}
=1
$