3/10x+4/5x+8=5

Solution for 3/10x+4/5x+8=5 equation:

3/10x+4/5x+8=5

We move all terms to the left:

3/10x+4/5x+8-(5)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


15x/50x^2+40x/50x^2+3=0

We multiply all the terms by the denominator


15x+40x+3*50x^2=0

We add all the numbers together, and all the variables

55x+3*50x^2=0

Wy multiply elements

150x^2+55x=0

a = 150; b = 55; c = 0;
Δ = b2-4ac
Δ = 552-4·150·0
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-55}{2*150}=\frac{-110}{300}
=-11/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+55}{2*150}=\frac{0}{300}
=0
$