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3.5x(x-2)=12-0.5x
We move all terms to the left:
3.5x(x-2)-(12-0.5x)=0
We add all the numbers together, and all the variables
3.5x(x-2)-(-0.5x+12)=0
We multiply parentheses
3x^2-6x-(-0.5x+12)=0
We get rid of parentheses
3x^2-6x+0.5x-12=0
We add all the numbers together, and all the variables
3x^2-5.5x-12=0
a = 3; b = -5.5; c = -12;
Δ = b2-4ac
Δ = -5.52-4·3·(-12)
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{-(-5.5)-\sqrt{174.25}}{2*3}=\frac{5.5-\sqrt{174.25}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.5)+\sqrt{174.25}}{2*3}=\frac{5.5+\sqrt{174.25}}{6} $
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