(2k-7)(5k+8)=0

Solution for (2k-7)(5k+8)=0 equation:

(2k-7)(5k+8)=0

We multiply parentheses ..

(+10k^2+16k-35k-56)=0

We get rid of parentheses

10k^2+16k-35k-56=0

We add all the numbers together, and all the variables

10k^2-19k-56=0

a = 10; b = -19; c = -56;
Δ = b2-4ac
Δ = -192-4·10·(-56)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-51}{2*10}=\frac{-32}{20}
=-1+3/5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+51}{2*10}=\frac{70}{20}
=3+1/2
$