-224x+21x^2=77

Solution for -224x+21x^2=77 equation:

-224x+21x^2=77

We move all terms to the left:

-224x+21x^2-(77)=0

a = 21; b = -224; c = -77;
Δ = b2-4ac
Δ = -2242-4·21·(-77)
Δ = 56644
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{56644}=238$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-224)-238}{2*21}=\frac{-14}{42}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-224)+238}{2*21}=\frac{462}{42}
=11
$