-11x+2x^2=21

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

-11x+2x^2=21

We move all terms to the left:

-11x+2x^2-(21)=0

a = 2; b = -11; c = -21;
Δ = b2-4ac
Δ = -112-4·2·(-21)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-17}{2*2}=\frac{-6}{4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+17}{2*2}=\frac{28}{4}
=7
$