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(9y-2)(2.1-7y)=0 equation

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Numerical solution:

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The solution

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          /21      \    
(9*y - 2)*|-- - 7*y| = 0
          \10      /
(2110−7y)(9y−2)=0\left(\frac{21}{10} - 7 y\right) \left(9 y - 2\right) = 0
Simplify
Detail solution
Expand the expression in the equation
(2110−7y)(9y−2)=0\left(\frac{21}{10} - 7 y\right) \left(9 y - 2\right) = 0
We get the quadratic equation
−63y2+329y10−215=0- 63 y^{2} + \frac{329 y}{10} - \frac{21}{5} = 0
This equation is of the form
a*y^2 + b*y + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
y1=D−b2ay_{1} = \frac{\sqrt{D} - b}{2 a}
y2=−D−b2ay_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=−63a = -63
b=32910b = \frac{329}{10}
c=−215c = - \frac{21}{5}
, then
D = b^2 - 4 * a * c = 

(329/10)^2 - 4 * (-63) * (-21/5) = 2401/100

Because D > 0, then the equation has two roots.
y1 = (-b + sqrt(D)) / (2*a)

y2 = (-b - sqrt(D)) / (2*a)

or
y1=29y_{1} = \frac{2}{9}
y2=310y_{2} = \frac{3}{10}
The graph
-12.5-10.0-7.5-5.0-2.50.02.55.07.510.012.515.0-100005000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
y1 = 2/9
y1=29y_{1} = \frac{2}{9} 
y2 = 3/10
y2=310y_{2} = \frac{3}{10} 
y2 = 3/10
Sum and product of roots [src] 
sum
2/9 + 3/10
29+310\frac{2}{9} + \frac{3}{10} 
=
47
--
90
4790\frac{47}{90} 
product
2*3 
----
9*10
2⋅39⋅10\frac{2 \cdot 3}{9 \cdot 10} 
=
1/15
115\frac{1}{15} 
1/15
Numerical answer [src] 
y1 = 0.222222222222222
y2 = 0.3
y2 = 0.3
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