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3x^2-5x+6.25=16.25
We move all terms to the left:
3x^2-5x+6.25-(16.25)=0
We add all the numbers together, and all the variables
3x^2-5x-10=0
a = 3; b = -5; c = -10;
Δ = b2-4ac
Δ = -52-4·3·(-10)
Δ = 145
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{145}}{2*3}=\frac{5-\sqrt{145}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{145}}{2*3}=\frac{5+\sqrt{145}}{6} $
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