-7k(k+5)=3k-(8k-1)

Solution for -7k(k+5)=3k-(8k-1) equation:

-7k(k+5)=3k-(8k-1)

We move all terms to the left:

-7k(k+5)-(3k-(8k-1))=0

We multiply parentheses

-7k^2-35k-(3k-(8k-1))=0


We calculate terms in parentheses: -(3k-(8k-1)), so:

3k-(8k-1)

We get rid of parentheses

3k-8k+1

We add all the numbers together, and all the variables

-5k+1

Back to the equation:

-(-5k+1)


We get rid of parentheses

-7k^2-35k+5k-1=0

We add all the numbers together, and all the variables

-7k^2-30k-1=0

a = -7; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·(-7)·(-1)
Δ = 872
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{872}=\sqrt{4*218}=\sqrt{4}*\sqrt{218}=2\sqrt{218}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{218}}{2*-7}=\frac{30-2\sqrt{218}}{-14}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{218}}{2*-7}=\frac{30+2\sqrt{218}}{-14}
$