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5x^2-12.5x-7.5/3-x=0
We add all the numbers together, and all the variables
5x^2-13.5x-7.5/3=0
We multiply all the terms by the denominator
5x^2*3-(13.5x)*3-7.5=0
We add all the numbers together, and all the variables
5x^2*3-(+13.5x)*3-7.5=0
We multiply parentheses
5x^2*3-39x-7.5=0
Wy multiply elements
15x^2-39x-7.5=0
a = 15; b = -39; c = -7.5;
Δ = b2-4ac
Δ = -392-4·15·(-7.5)
Δ = 1971
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1971}=\sqrt{9*219}=\sqrt{9}*\sqrt{219}=3\sqrt{219}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-3\sqrt{219}}{2*15}=\frac{39-3\sqrt{219}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+3\sqrt{219}}{2*15}=\frac{39+3\sqrt{219}}{30} $
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