2.5x+-15/6x=0

Solution for 2.5x+-15/6x=0 equation:

2.5x+-15/6x=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

2.5x-15/6x=0

We multiply all the terms by the denominator


(2.5x)*6x-15=0

We add all the numbers together, and all the variables

(+2.5x)*6x-15=0

We multiply parentheses

12x^2-15=0

a = 12; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·12·(-15)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*12}=\frac{0-12\sqrt{5}}{24}
=-\frac{12\sqrt{5}}{24}
=-\frac{\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*12}=\frac{0+12\sqrt{5}}{24}
=\frac{12\sqrt{5}}{24}
=\frac{\sqrt{5}}{2}
$