6.25x-1/4x+2.25+7.3x=0

Solution for 6.25x-1/4x+2.25+7.3x=0 equation:

6.25x-1/4x+2.25+7.3x=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

13.55x-1/4x+2.25=0

We multiply all the terms by the denominator


(13.55x)*4x+(2.25)*4x-1=0

We add all the numbers together, and all the variables

(+13.55x)*4x+(2.25)*4x-1=0

We multiply parentheses

52x^2+9x-1=0

a = 52; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·52·(-1)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-17}{2*52}=\frac{-26}{104}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+17}{2*52}=\frac{8}{104}
=1/13
$