7(x+9)3x-8,x=9

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Solution for 7(x+9)3x-8,x=9 equation:



7(x+9)3x-8.x=9
We move all terms to the left:
7(x+9)3x-8.x-(9)=0
We add all the numbers together, and all the variables
-8x+7(x+9)3x-9=0
We multiply parentheses
21x^2-8x+189x-9=0
We add all the numbers together, and all the variables
21x^2+181x-9=0
a = 21; b = 181; c = -9;
Δ = b2-4ac
Δ = 1812-4·21·(-9)
Δ = 33517
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:
$\sqrt{\Delta}=\sqrt{33517}=\sqrt{121*277}=\sqrt{121}*\sqrt{277}=11\sqrt{277}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(181)-11\sqrt{277}}{2*21}=\frac{-181-11\sqrt{277}}{42} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(181)+11\sqrt{277}}{2*21}=\frac{-181+11\sqrt{277}}{42} $

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