9x(x+1)=25+x

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Solution for 9x(x+1)=25+x equation:



9x(x+1)=25+x
We move all terms to the left:
9x(x+1)-(25+x)=0
We add all the numbers together, and all the variables
9x(x+1)-(x+25)=0
We multiply parentheses
9x^2+9x-(x+25)=0
We get rid of parentheses
9x^2+9x-x-25=0
We add all the numbers together, and all the variables
9x^2+8x-25=0
a = 9; b = 8; c = -25;
Δ = b2-4ac
Δ = 82-4·9·(-25)
Δ = 964
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:
$\sqrt{\Delta}=\sqrt{964}=\sqrt{4*241}=\sqrt{4}*\sqrt{241}=2\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{241}}{2*9}=\frac{-8-2\sqrt{241}}{18} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{241}}{2*9}=\frac{-8+2\sqrt{241}}{18} $

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