11+10x-2x^2=0

Solution for 11+10x-2x^2=0 equation:

11+10x-2x^2=0

a = -2; b = 10; c = +11;
Δ = b2-4ac
Δ = 102-4·(-2)·11
Δ = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{47}}{2*-2}=\frac{-10-2\sqrt{47}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{47}}{2*-2}=\frac{-10+2\sqrt{47}}{-4}
$