x+2.5x+(1)/(2)x=7.5

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Solution for x+2.5x+(1)/(2)x=7.5 equation: 



x+2.5x+(1)/(2)x=7.5

We move all terms to the left:

x+2.5x+(1)/(2)x-(7.5)=0



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



We add all the numbers together, and all the variables

3.5x+1/2x-7.5=0

We multiply all the terms by the denominator


(3.5x)*2x-(7.5)*2x+1=0

We add all the numbers together, and all the variables

(+3.5x)*2x-(7.5)*2x+1=0

We multiply parentheses

6x^2-15x+1=0

a = 6; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·6·1
Δ = 201
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{-(-15)-\sqrt{201}}{2*6}=\frac{15-\sqrt{201}}{12}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{201}}{2*6}=\frac{15+\sqrt{201}}{12}
$

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