0.3+5.24=3/2x+2.24x

Solution for 0.3+5.24=3/2x+2.24x equation:

0.3+5.24=3/2x+2.24x

We move all terms to the left:

0.3+5.24-(3/2x+2.24x)=0


Domain of the equation: 2x+2.24x)!=0

x∈R


We add all the numbers together, and all the variables

-(+2.24x+3/2x)+0.3+5.24=0

We add all the numbers together, and all the variables

-(+2.24x+3/2x)+5.54=0

We get rid of parentheses

-2.24x-3/2x+5.54=0

We multiply all the terms by the denominator


-(2.24x)*2x+(5.54)*2x-3=0

We add all the numbers together, and all the variables

-(+2.24x)*2x+(5.54)*2x-3=0

We multiply parentheses

-4x^2+11.08x-3=0

a = -4; b = 11.08; c = -3;
Δ = b2-4ac
Δ = 11.082-4·(-4)·(-3)
Δ = 74.7664
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{-(11.08)-\sqrt{74.7664}}{2*-4}=\frac{-11.08-\sqrt{74.7664}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11.08)+\sqrt{74.7664}}{2*-4}=\frac{-11.08+\sqrt{74.7664}}{-8}
$