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(x-1)(8x-1)=18x
We move all terms to the left:
(x-1)(8x-1)-(18x)=0
We add all the numbers together, and all the variables
-18x+(x-1)(8x-1)=0
We multiply parentheses ..
(+8x^2-1x-8x+1)-18x=0
We get rid of parentheses
8x^2-1x-8x-18x+1=0
We add all the numbers together, and all the variables
8x^2-27x+1=0
a = 8; b = -27; c = +1;
Δ = b2-4ac
Δ = -272-4·8·1
Δ = 697
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{-(-27)-\sqrt{697}}{2*8}=\frac{27-\sqrt{697}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{697}}{2*8}=\frac{27+\sqrt{697}}{16} $
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