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10x^2+5x=1.5
We move all terms to the left:
10x^2+5x-(1.5)=0
We add all the numbers together, and all the variables
10x^2+5x-1.5=0
a = 10; b = 5; c = -1.5;
Δ = b2-4ac
Δ = 52-4·10·(-1.5)
Δ = 85
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)-\sqrt{85}}{2*10}=\frac{-5-\sqrt{85}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{85}}{2*10}=\frac{-5+\sqrt{85}}{20} $
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