7x2+18x-19=0

Solution for 7x2+18x-19=0 equation:

7x^2+18x-19=0

a = 7; b = 18; c = -19;
Δ = b2-4ac
Δ = 182-4·7·(-19)
Δ = 856
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:

$\sqrt{\Delta}=\sqrt{856}=\sqrt{4*214}=\sqrt{4}*\sqrt{214}=2\sqrt{214}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{214}}{2*7}=\frac{-18-2\sqrt{214}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{214}}{2*7}=\frac{-18+2\sqrt{214}}{14}
$