x2-9x-19/14=0

Solution for x2-9x-19/14=0 equation:

x2-9x-19/14=0

We add all the numbers together, and all the variables

x^2-9x-19/14=0

We multiply all the terms by the denominator


x^2*14-9x*14-19=0

Wy multiply elements

14x^2-126x-19=0

a = 14; b = -126; c = -19;
Δ = b2-4ac
Δ = -1262-4·14·(-19)
Δ = 16940
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{16940}=\sqrt{484*35}=\sqrt{484}*\sqrt{35}=22\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-22\sqrt{35}}{2*14}=\frac{126-22\sqrt{35}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+22\sqrt{35}}{2*14}=\frac{126+22\sqrt{35}}{28}
$