(n-7)2n-3=0

Solution for (n-7)2n-3=0 equation:

(n-7)2n-3=0

We multiply parentheses

2n^2-14n-3=0

a = 2; b = -14; c = -3;
Δ = b2-4ac
Δ = -142-4·2·(-3)
Δ = 220
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{55}}{2*2}=\frac{14-2\sqrt{55}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{55}}{2*2}=\frac{14+2\sqrt{55}}{4}
$