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(14x-65)(6x+39)=x
We move all terms to the left:
(14x-65)(6x+39)-(x)=0
We add all the numbers together, and all the variables
-1x+(14x-65)(6x+39)=0
We multiply parentheses ..
(+84x^2+546x-390x-2535)-1x=0
We get rid of parentheses
84x^2+546x-390x-1x-2535=0
We add all the numbers together, and all the variables
84x^2+155x-2535=0
a = 84; b = 155; c = -2535;
Δ = b2-4ac
Δ = 1552-4·84·(-2535)
Δ = 875785
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{-(155)-\sqrt{875785}}{2*84}=\frac{-155-\sqrt{875785}}{168} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(155)+\sqrt{875785}}{2*84}=\frac{-155+\sqrt{875785}}{168} $
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