21x^2=16-50x

Solution for 21x^2=16-50x equation:

21x^2=16-50x

We move all terms to the left:

21x^2-(16-50x)=0

We add all the numbers together, and all the variables

21x^2-(-50x+16)=0

We get rid of parentheses

21x^2+50x-16=0

a = 21; b = 50; c = -16;
Δ = b2-4ac
Δ = 502-4·21·(-16)
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-62}{2*21}=\frac{-112}{42}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+62}{2*21}=\frac{12}{42}
=2/7
$