7n^2-68n+45=0

Solution for 7n^2-68n+45=0 equation:

7n^2-68n+45=0

a = 7; b = -68; c = +45;
Δ = b2-4ac
Δ = -682-4·7·45
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-58}{2*7}=\frac{10}{14}
=5/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+58}{2*7}=\frac{126}{14}
=9
$