3/5x-1/4x+14=7/10

Solution for 3/5x-1/4x+14=7/10 equation:

3/5x-1/4x+14=7/10

We move all terms to the left:

3/5x-1/4x+14-(7/10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-1/4x+14-(+7/10)=0

We get rid of parentheses

3/5x-1/4x+14-7/10=0

We calculate fractions


(-560x^2)/200x^2+120x/200x^2+(-50x)/200x^2+14=0

We multiply all the terms by the denominator


(-560x^2)+120x+(-50x)+14*200x^2=0

Wy multiply elements

(-560x^2)+2800x^2+120x+(-50x)=0

We get rid of parentheses

-560x^2+2800x^2+120x-50x=0

We add all the numbers together, and all the variables

2240x^2+70x=0

a = 2240; b = 70; c = 0;
Δ = b2-4ac
Δ = 702-4·2240·0
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-70}{2*2240}=\frac{-140}{4480}
=-1/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+70}{2*2240}=\frac{0}{4480}
=0
$