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(2x-9)(3x+2)=x
We move all terms to the left:
(2x-9)(3x+2)-(x)=0
We add all the numbers together, and all the variables
-1x+(2x-9)(3x+2)=0
We multiply parentheses ..
(+6x^2+4x-27x-18)-1x=0
We get rid of parentheses
6x^2+4x-27x-1x-18=0
We add all the numbers together, and all the variables
6x^2-24x-18=0
a = 6; b = -24; c = -18;
Δ = b2-4ac
Δ = -242-4·6·(-18)
Δ = 1008
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{7}}{2*6}=\frac{24-12\sqrt{7}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{7}}{2*6}=\frac{24+12\sqrt{7}}{12} $
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