3/5x+4=3/10x+7

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

3/5x+4=3/10x+7

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x+7)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


30x/50x^2+(-15x)/50x^2-7+4=0

We add all the numbers together, and all the variables

30x/50x^2+(-15x)/50x^2-3=0

We multiply all the terms by the denominator


30x+(-15x)-3*50x^2=0

Wy multiply elements

-150x^2+30x+(-15x)=0

We get rid of parentheses

-150x^2+30x-15x=0

We add all the numbers together, and all the variables

-150x^2+15x=0

a = -150; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-150)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-150}=\frac{-30}{-300}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-150}=\frac{0}{-300}
=0
$