11x^2+34x-21=0

Solution for 11x^2+34x-21=0 equation:

11x^2+34x-21=0

a = 11; b = 34; c = -21;
Δ = b2-4ac
Δ = 342-4·11·(-21)
Δ = 2080
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:

$\sqrt{\Delta}=\sqrt{2080}=\sqrt{16*130}=\sqrt{16}*\sqrt{130}=4\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-4\sqrt{130}}{2*11}=\frac{-34-4\sqrt{130}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+4\sqrt{130}}{2*11}=\frac{-34+4\sqrt{130}}{22}
$