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0.5x^2+1.5=26
We move all terms to the left:
0.5x^2+1.5-(26)=0
We add all the numbers together, and all the variables
0.5x^2-24.5=0
a = 0.5; b = 0; c = -24.5;
Δ = b2-4ac
Δ = 02-4·0.5·(-24.5)
Δ = 49
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{49}=7$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-7}{2*0.5}=\frac{-7}{1} =-7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+7}{2*0.5}=\frac{7}{1} =7 $
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