(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

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^2-23k-35=0

a = 4; b = -23; c = -35;
Δ = b2-4ac
Δ = -232-4·4·(-35)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-33}{2*4}=\frac{-10}{8}
=-1+1/4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+33}{2*4}=\frac{56}{8}
=7
$