7/10(30x)+19=3/5(35x)+12

Solution for 7/10(30x)+19=3/5(35x)+12 equation:

7/10(30x)+19=3/5(35x)+12

We move all terms to the left:

7/10(30x)+19-(3/5(35x)+12)=0


Domain of the equation: 1030x!=0

x!=0/1030

x!=0

x∈R



Domain of the equation: 535x+12)!=0

x∈R


We get rid of parentheses

7/1030x-3/535x-12+19=0

We calculate fractions


3745x/551050x^2+(-3090x)/551050x^2-12+19=0

We add all the numbers together, and all the variables

3745x/551050x^2+(-3090x)/551050x^2+7=0

We multiply all the terms by the denominator


3745x+(-3090x)+7*551050x^2=0

Wy multiply elements

3857350x^2+3745x+(-3090x)=0

We get rid of parentheses

3857350x^2+3745x-3090x=0

We add all the numbers together, and all the variables

3857350x^2+655x=0

a = 3857350; b = 655; c = 0;
Δ = b2-4ac
Δ = 6552-4·3857350·0
Δ = 429025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{429025}=655$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(655)-655}{2*3857350}=\frac{-1310}{7714700}
=-131/771470
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(655)+655}{2*3857350}=\frac{0}{7714700}
=0
$