7x^2+186x-225=0

Solution for 7x^2+186x-225=0 equation:

7x^2+186x-225=0

a = 7; b = 186; c = -225;
Δ = b2-4ac
Δ = 1862-4·7·(-225)
Δ = 40896
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:

$\sqrt{\Delta}=\sqrt{40896}=\sqrt{576*71}=\sqrt{576}*\sqrt{71}=24\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(186)-24\sqrt{71}}{2*7}=\frac{-186-24\sqrt{71}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(186)+24\sqrt{71}}{2*7}=\frac{-186+24\sqrt{71}}{14}
$