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x^2+5x+6.25=3.75
We move all terms to the left:
x^2+5x+6.25-(3.75)=0
We add all the numbers together, and all the variables
x^2+5x+2.5=0
a = 1; b = 5; c = +2.5;
Δ = b2-4ac
Δ = 52-4·1·2.5
Δ = 15
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{15}}{2*1}=\frac{-5-\sqrt{15}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{15}}{2*1}=\frac{-5+\sqrt{15}}{2} $
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