11x*x+6x-21=0

Solution for 11x*x+6x-21=0 equation:

11x*x+6x-21=0

We add all the numbers together, and all the variables

6x+11x*x-21=0

Wy multiply elements

11x^2+6x-21=0

a = 11; b = 6; c = -21;
Δ = b2-4ac
Δ = 62-4·11·(-21)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-8\sqrt{15}}{2*11}=\frac{-6-8\sqrt{15}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+8\sqrt{15}}{2*11}=\frac{-6+8\sqrt{15}}{22}
$