20k(k+2)=7k-10

Solution for 20k(k+2)=7k-10 equation:

20k(k+2)=7k-10

We move all terms to the left:

20k(k+2)-(7k-10)=0

We multiply parentheses

20k^2+40k-(7k-10)=0

We get rid of parentheses

20k^2+40k-7k+10=0

We add all the numbers together, and all the variables

20k^2+33k+10=0

a = 20; b = 33; c = +10;
Δ = b2-4ac
Δ = 332-4·20·10
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-17}{2*20}=\frac{-50}{40}
=-1+1/4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+17}{2*20}=\frac{-16}{40}
=-2/5
$