19+1.50x=15+2/75x

Solution for 19+1.50x=15+2/75x equation:

19+1.50x=15+2/75x

We move all terms to the left:

19+1.50x-(15+2/75x)=0


Domain of the equation: 75x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1.50x-(2/75x+15)+19=0

We get rid of parentheses

1.50x-2/75x-15+19=0

We multiply all the terms by the denominator


(1.50x)*75x-15*75x+19*75x-2=0

We add all the numbers together, and all the variables

(+1.50x)*75x-15*75x+19*75x-2=0

We multiply parentheses

75x^2-15*75x+19*75x-2=0

Wy multiply elements

75x^2-1125x+1425x-2=0

We add all the numbers together, and all the variables

75x^2+300x-2=0

a = 75; b = 300; c = -2;
Δ = b2-4ac
Δ = 3002-4·75·(-2)
Δ = 90600
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:

$\sqrt{\Delta}=\sqrt{90600}=\sqrt{100*906}=\sqrt{100}*\sqrt{906}=10\sqrt{906}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-10\sqrt{906}}{2*75}=\frac{-300-10\sqrt{906}}{150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+10\sqrt{906}}{2*75}=\frac{-300+10\sqrt{906}}{150}
$