(2n-7)(5n+6)=0

Solution for (2n-7)(5n+6)=0 equation:

(2n-7)(5n+6)=0

We multiply parentheses ..

(+10n^2+12n-35n-42)=0

We get rid of parentheses

10n^2+12n-35n-42=0

We add all the numbers together, and all the variables

10n^2-23n-42=0

a = 10; b = -23; c = -42;
Δ = b2-4ac
Δ = -232-4·10·(-42)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-47}{2*10}=\frac{-24}{20}
=-1+1/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+47}{2*10}=\frac{70}{20}
=3+1/2
$