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(9x+14)(3x-2)=x
We move all terms to the left:
(9x+14)(3x-2)-(x)=0
We add all the numbers together, and all the variables
-1x+(9x+14)(3x-2)=0
We multiply parentheses ..
(+27x^2-18x+42x-28)-1x=0
We get rid of parentheses
27x^2-18x+42x-1x-28=0
We add all the numbers together, and all the variables
27x^2+23x-28=0
a = 27; b = 23; c = -28;
Δ = b2-4ac
Δ = 232-4·27·(-28)
Δ = 3553
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{-(23)-\sqrt{3553}}{2*27}=\frac{-23-\sqrt{3553}}{54} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{3553}}{2*27}=\frac{-23+\sqrt{3553}}{54} $
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