7,5-3/2x=4,5-x

Solution for 7,5-3/2x=4,5-x equation:

7.5-3/2x=4.5-x

We move all terms to the left:

7.5-3/2x-(4.5-x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-3/2x-(-1x+4.5)+7.5=0

We get rid of parentheses

-3/2x+1x-4.5+7.5=0

We multiply all the terms by the denominator


1x*2x-(4.5)*2x+(7.5)*2x-3=0

We multiply parentheses

1x*2x-9x+15x-3=0

Wy multiply elements

2x^2-9x+15x-3=0

We add all the numbers together, and all the variables

2x^2+6x-3=0

a = 2; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·2·(-3)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{15}}{2*2}=\frac{-6-2\sqrt{15}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{15}}{2*2}=\frac{-6+2\sqrt{15}}{4}
$