3/5x+19-3/20x=7

Solution for 3/5x+19-3/20x=7 equation:

3/5x+19-3/20x=7

We move all terms to the left:

3/5x+19-3/20x-(7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 20x!=0

x!=0/20

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-3/20x+12=0

We calculate fractions


60x/100x^2+(-15x)/100x^2+12=0

We multiply all the terms by the denominator


60x+(-15x)+12*100x^2=0

Wy multiply elements

1200x^2+60x+(-15x)=0

We get rid of parentheses

1200x^2+60x-15x=0

We add all the numbers together, and all the variables

1200x^2+45x=0

a = 1200; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·1200·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*1200}=\frac{-90}{2400}
=-3/80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*1200}=\frac{0}{2400}
=0
$