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x2-1.5x-52=0
We add all the numbers together, and all the variables
x^2-1.5x-52=0
a = 1; b = -1.5; c = -52;
Δ = b2-4ac
Δ = -1.52-4·1·(-52)
Δ = 210.25
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{-(-1.5)-\sqrt{210.25}}{2*1}=\frac{1.5-\sqrt{210.25}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{210.25}}{2*1}=\frac{1.5+\sqrt{210.25}}{2} $
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