(5n+7)(n-2)=0

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

(5n+7)(n-2)=0

We multiply parentheses ..

(+5n^2-10n+7n-14)=0

We get rid of parentheses

5n^2-10n+7n-14=0

We add all the numbers together, and all the variables

5n^2-3n-14=0

a = 5; b = -3; c = -14;
Δ = b2-4ac
Δ = -32-4·5·(-14)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-17}{2*5}=\frac{-14}{10}
=-1+2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+17}{2*5}=\frac{20}{10}
=2
$