4/5x+7=7/10x-9

Solution for 4/5x+7=7/10x-9 equation:

4/5x+7=7/10x-9

We move all terms to the left:

4/5x+7-(7/10x-9)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x-9)!=0

x∈R


We get rid of parentheses

4/5x-7/10x+9+7=0

We calculate fractions


40x/50x^2+(-35x)/50x^2+9+7=0

We add all the numbers together, and all the variables

40x/50x^2+(-35x)/50x^2+16=0

We multiply all the terms by the denominator


40x+(-35x)+16*50x^2=0

Wy multiply elements

800x^2+40x+(-35x)=0

We get rid of parentheses

800x^2+40x-35x=0

We add all the numbers together, and all the variables

800x^2+5x=0

a = 800; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·800·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*800}=\frac{-10}{1600}
=-1/160
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*800}=\frac{0}{1600}
=0
$