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(9x-13)(6x+23)=x
We move all terms to the left:
(9x-13)(6x+23)-(x)=0
We add all the numbers together, and all the variables
-1x+(9x-13)(6x+23)=0
We multiply parentheses ..
(+54x^2+207x-78x-299)-1x=0
We get rid of parentheses
54x^2+207x-78x-1x-299=0
We add all the numbers together, and all the variables
54x^2+128x-299=0
a = 54; b = 128; c = -299;
Δ = b2-4ac
Δ = 1282-4·54·(-299)
Δ = 80968
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{80968}=\sqrt{4*20242}=\sqrt{4}*\sqrt{20242}=2\sqrt{20242}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-2\sqrt{20242}}{2*54}=\frac{-128-2\sqrt{20242}}{108} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+2\sqrt{20242}}{2*54}=\frac{-128+2\sqrt{20242}}{108} $
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