5x^2-12.5x-7.5/3-x=0

Solution for 5x^2-12.5x-7.5/3-x=0 equation:

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}
$