(-9k+8)(6k-7)=0

Solution for (-9k+8)(6k-7)=0 equation:

(-9k+8)(6k-7)=0

We multiply parentheses ..

(-54k^2+63k+48k-56)=0

We get rid of parentheses

-54k^2+63k+48k-56=0

We add all the numbers together, and all the variables

-54k^2+111k-56=0

a = -54; b = 111; c = -56;
Δ = b2-4ac
Δ = 1112-4·(-54)·(-56)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(111)-15}{2*-54}=\frac{-126}{-108}
=1+1/6
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(111)+15}{2*-54}=\frac{-96}{-108}
=8/9
$