4/5x-4=-9/10x+1

Solution for 4/5x-4=-9/10x+1 equation:

4/5x-4=-9/10x+1

We move all terms to the left:

4/5x-4-(-9/10x+1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x+1)!=0

x∈R


We get rid of parentheses

4/5x+9/10x-1-4=0

We calculate fractions


40x/50x^2+45x/50x^2-1-4=0

We add all the numbers together, and all the variables

40x/50x^2+45x/50x^2-5=0

We multiply all the terms by the denominator


40x+45x-5*50x^2=0

We add all the numbers together, and all the variables

85x-5*50x^2=0

Wy multiply elements

-250x^2+85x=0

a = -250; b = 85; c = 0;
Δ = b2-4ac
Δ = 852-4·(-250)·0
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(85)-85}{2*-250}=\frac{-170}{-500}
=17/50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+85}{2*-250}=\frac{0}{-500}
=0
$