7x^2-22x-65=0

Solution for 7x^2-22x-65=0 equation:

7x^2-22x-65=0

a = 7; b = -22; c = -65;
Δ = b2-4ac
Δ = -222-4·7·(-65)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-48}{2*7}=\frac{-26}{14}
=-1+6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+48}{2*7}=\frac{70}{14}
=5
$