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0.5x+x+3=-0.5x^2-2x+7
We move all terms to the left:
0.5x+x+3-(-0.5x^2-2x+7)=0
We add all the numbers together, and all the variables
-(-0.5x^2-2x+7)+1.5x+3=0
We get rid of parentheses
0.5x^2+2x+1.5x-7+3=0
We add all the numbers together, and all the variables
0.5x^2+3.5x-4=0
a = 0.5; b = 3.5; c = -4;
Δ = b2-4ac
Δ = 3.52-4·0.5·(-4)
Δ = 20.25
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{-(3.5)-\sqrt{20.25}}{2*0.5}=\frac{-3.5-\sqrt{20.25}}{1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3.5)+\sqrt{20.25}}{2*0.5}=\frac{-3.5+\sqrt{20.25}}{1} $
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