2.5x+1/2x=-33

Solution for 2.5x+1/2x=-33 equation:

2.5x+1/2x=-33

We move all terms to the left:

2.5x+1/2x-(-33)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2.5x+1/2x+33=0

We multiply all the terms by the denominator


(2.5x)*2x+33*2x+1=0

We add all the numbers together, and all the variables

(+2.5x)*2x+33*2x+1=0

We multiply parentheses

4x^2+33*2x+1=0

Wy multiply elements

4x^2+66x+1=0

a = 4; b = 66; c = +1;
Δ = b2-4ac
Δ = 662-4·4·1
Δ = 4340
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:

$\sqrt{\Delta}=\sqrt{4340}=\sqrt{4*1085}=\sqrt{4}*\sqrt{1085}=2\sqrt{1085}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-2\sqrt{1085}}{2*4}=\frac{-66-2\sqrt{1085}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+2\sqrt{1085}}{2*4}=\frac{-66+2\sqrt{1085}}{8}
$