7+7/10x=17/20x

Solution for 7+7/10x=17/20x equation:

7+7/10x=17/20x

We move all terms to the left:

7+7/10x-(17/20x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 20x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7/10x-(+17/20x)+7=0

We get rid of parentheses

7/10x-17/20x+7=0

We calculate fractions


140x/200x^2+(-170x)/200x^2+7=0

We multiply all the terms by the denominator


140x+(-170x)+7*200x^2=0

Wy multiply elements

1400x^2+140x+(-170x)=0

We get rid of parentheses

1400x^2+140x-170x=0

We add all the numbers together, and all the variables

1400x^2-30x=0

a = 1400; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·1400·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*1400}=\frac{0}{2800}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*1400}=\frac{60}{2800}
=3/140
$