x^2+11x-29.75=0

Solution for x^2+11x-29.75=0 equation:

x^2+11x-29.75=0

a = 1; b = 11; c = -29.75;
Δ = b2-4ac
Δ = 112-4·1·(-29.75)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-4\sqrt{15}}{2*1}=\frac{-11-4\sqrt{15}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+4\sqrt{15}}{2*1}=\frac{-11+4\sqrt{15}}{2}
$