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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


40x/50x^2+15x/50x^2-4=0

We multiply all the terms by the denominator


40x+15x-4*50x^2=0

We add all the numbers together, and all the variables

55x-4*50x^2=0

Wy multiply elements

-200x^2+55x=0

a = -200; b = 55; c = 0;
Δ = b2-4ac
Δ = 552-4·(-200)·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*-200}=\frac{-110}{-400}
=11/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+55}{2*-200}=\frac{0}{-400}
=0
$