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(8x+11)(12x-1)=x
We move all terms to the left:
(8x+11)(12x-1)-(x)=0
We add all the numbers together, and all the variables
-1x+(8x+11)(12x-1)=0
We multiply parentheses ..
(+96x^2-8x+132x-11)-1x=0
We get rid of parentheses
96x^2-8x+132x-1x-11=0
We add all the numbers together, and all the variables
96x^2+123x-11=0
a = 96; b = 123; c = -11;
Δ = b2-4ac
Δ = 1232-4·96·(-11)
Δ = 19353
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{-(123)-\sqrt{19353}}{2*96}=\frac{-123-\sqrt{19353}}{192} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(123)+\sqrt{19353}}{2*96}=\frac{-123+\sqrt{19353}}{192} $
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