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(11-3x)(8.5-3x)=x
We move all terms to the left:
(11-3x)(8.5-3x)-(x)=0
We add all the numbers together, and all the variables
(-3x+11)(-3x+8.5)-x=0
We add all the numbers together, and all the variables
-1x+(-3x+11)(-3x+8.5)=0
We multiply parentheses ..
(+9x^2-25.5x-33x+93.5)-1x=0
We get rid of parentheses
9x^2-25.5x-33x-1x+93.5=0
We add all the numbers together, and all the variables
9x^2-59.5x+93.5=0
a = 9; b = -59.5; c = +93.5;
Δ = b2-4ac
Δ = -59.52-4·9·93.5
Δ = 174.25
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{-(-59.5)-\sqrt{174.25}}{2*9}=\frac{59.5-\sqrt{174.25}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59.5)+\sqrt{174.25}}{2*9}=\frac{59.5+\sqrt{174.25}}{18} $
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