7.5+30/x=1.2x+7.5

Solution for 7.5+30/x=1.2x+7.5 equation:

7.5+30/x=1.2x+7.5

We move all terms to the left:

7.5+30/x-(1.2x+7.5)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

30/x-1.2x-7.5+7.5=0

We multiply all the terms by the denominator


-(1.2x)*x-(7.5)*x+(7.5)*x+30=0

We add all the numbers together, and all the variables

-(+1.2x)*x-(7.5)*x+(7.5)*x+30=0

We multiply parentheses

-x^2-7.5x+7.5x+30=0

We add all the numbers together, and all the variables

-1x^2+30=0

a = -1; b = 0; c = +30;
Δ = b2-4ac
Δ = 02-4·(-1)·30
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*-1}=\frac{0-2\sqrt{30}}{-2}
=-\frac{2\sqrt{30}}{-2}
=-\frac{\sqrt{30}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*-1}=\frac{0+2\sqrt{30}}{-2}
=\frac{2\sqrt{30}}{-2}
=\frac{\sqrt{30}}{-1}
$