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5x(x-2)=2(x+6)
We move all terms to the left:
5x(x-2)-(2(x+6))=0
We multiply parentheses
5x^2-10x-(2(x+6))=0
We calculate terms in parentheses: -(2(x+6)), so:We get rid of parentheses
2(x+6)
We multiply parentheses
2x+12
Back to the equation:
-(2x+12)
5x^2-10x-2x-12=0
We add all the numbers together, and all the variables
5x^2-12x-12=0
a = 5; b = -12; c = -12;
Δ = b2-4ac
Δ = -122-4·5·(-12)
Δ = 384
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{6}}{2*5}=\frac{12-8\sqrt{6}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{6}}{2*5}=\frac{12+8\sqrt{6}}{10} $
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