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(7x-9)(2x+1)=x
We move all terms to the left:
(7x-9)(2x+1)-(x)=0
We add all the numbers together, and all the variables
-1x+(7x-9)(2x+1)=0
We multiply parentheses ..
(+14x^2+7x-18x-9)-1x=0
We get rid of parentheses
14x^2+7x-18x-1x-9=0
We add all the numbers together, and all the variables
14x^2-12x-9=0
a = 14; b = -12; c = -9;
Δ = b2-4ac
Δ = -122-4·14·(-9)
Δ = 648
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-18\sqrt{2}}{2*14}=\frac{12-18\sqrt{2}}{28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+18\sqrt{2}}{2*14}=\frac{12+18\sqrt{2}}{28} $
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