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11x-3x(x-2)=8x+3
We move all terms to the left:
11x-3x(x-2)-(8x+3)=0
We multiply parentheses
-3x^2+11x+6x-(8x+3)=0
We get rid of parentheses
-3x^2+11x+6x-8x-3=0
We add all the numbers together, and all the variables
-3x^2+9x-3=0
a = -3; b = 9; c = -3;
Δ = b2-4ac
Δ = 92-4·(-3)·(-3)
Δ = 45
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{5}}{2*-3}=\frac{-9-3\sqrt{5}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{5}}{2*-3}=\frac{-9+3\sqrt{5}}{-6} $
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