-7n^2+38n-40=0

Solution for -7n^2+38n-40=0 equation:

-7n^2+38n-40=0

a = -7; b = 38; c = -40;
Δ = b2-4ac
Δ = 382-4·(-7)·(-40)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-18}{2*-7}=\frac{-56}{-14}
=+4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+18}{2*-7}=\frac{-20}{-14}
=1+3/7
$