(2x-3)*(4x+9)=x

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Solution for (2x-3)*(4x+9)=x equation:



(2x-3)(4x+9)=x
We move all terms to the left:
(2x-3)(4x+9)-(x)=0
We add all the numbers together, and all the variables
-1x+(2x-3)(4x+9)=0
We multiply parentheses ..
(+8x^2+18x-12x-27)-1x=0
We get rid of parentheses
8x^2+18x-12x-1x-27=0
We add all the numbers together, and all the variables
8x^2+5x-27=0
a = 8; b = 5; c = -27;
Δ = b2-4ac
Δ = 52-4·8·(-27)
Δ = 889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{889}}{2*8}=\frac{-5-\sqrt{889}}{16} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{889}}{2*8}=\frac{-5+\sqrt{889}}{16} $

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