(4k+5)(k+7)=0*

Solution for (4k+5)(k+7)=0* equation:

(4k+5)(k+7)=0*

We move all terms to the left:

(4k+5)(k+7)-(0*)=0

We add all the numbers together, and all the variables

(4k+5)(k+7)-0=0

We add all the numbers together, and all the variables

(4k+5)(k+7)=0

We multiply parentheses ..

(+4k^2+28k+5k+35)=0

We get rid of parentheses

4k^2+28k+5k+35=0

We add all the numbers together, and all the variables

4k^2+33k+35=0

a = 4; b = 33; c = +35;
Δ = b2-4ac
Δ = 332-4·4·35
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-23}{2*4}=\frac{-56}{8}
=-7
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+23}{2*4}=\frac{-10}{8}
=-1+1/4
$