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3x(x-2)=5x+8
We move all terms to the left:
3x(x-2)-(5x+8)=0
We multiply parentheses
3x^2-6x-(5x+8)=0
We get rid of parentheses
3x^2-6x-5x-8=0
We add all the numbers together, and all the variables
3x^2-11x-8=0
a = 3; b = -11; c = -8;
Δ = b2-4ac
Δ = -112-4·3·(-8)
Δ = 217
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{-(-11)-\sqrt{217}}{2*3}=\frac{11-\sqrt{217}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{217}}{2*3}=\frac{11+\sqrt{217}}{6} $
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