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0.5(x+2)=0.1x+0.6x(x-3)
We move all terms to the left:
0.5(x+2)-(0.1x+0.6x(x-3))=0
We multiply parentheses
0.5x-(0.1x+0.6x(x-3))+1=0
We calculate terms in parentheses: -(0.1x+0.6x(x-3)), so:We get rid of parentheses
0.1x+0.6x(x-3)
We multiply parentheses
0x^2+0.1x+0x
We add all the numbers together, and all the variables
x^2+1.1x
Back to the equation:
-(x^2+1.1x)
-x^2+0.5x-1.1x+1=0
We add all the numbers together, and all the variables
-1x^2-0.6x+1=0
a = -1; b = -0.6; c = +1;
Δ = b2-4ac
Δ = -0.62-4·(-1)·1
Δ = 4.36
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{-(-0.6)-\sqrt{4.36}}{2*-1}=\frac{0.6-\sqrt{4.36}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.6)+\sqrt{4.36}}{2*-1}=\frac{0.6+\sqrt{4.36}}{-2} $
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