9/10u-1/3=4/25u+4

Solution for 9/10u-1/3=4/25u+4 equation:

9/10u-1/3=4/25u+4

We move all terms to the left:

9/10u-1/3-(4/25u+4)=0


Domain of the equation: 10u!=0

u!=0/10

u!=0

u∈R



Domain of the equation: 25u+4)!=0

u∈R


We get rid of parentheses

9/10u-4/25u-4-1/3=0

We calculate fractions


(-500u^2)/2250u^2+2025u/2250u^2+(-360u)/2250u^2-4=0

We multiply all the terms by the denominator


(-500u^2)+2025u+(-360u)-4*2250u^2=0

Wy multiply elements

(-500u^2)-9000u^2+2025u+(-360u)=0

We get rid of parentheses

-500u^2-9000u^2+2025u-360u=0

We add all the numbers together, and all the variables

-9500u^2+1665u=0

a = -9500; b = 1665; c = 0;
Δ = b2-4ac
Δ = 16652-4·(-9500)·0
Δ = 2772225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2772225}=1665$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1665)-1665}{2*-9500}=\frac{-3330}{-19000}
=333/1900
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1665)+1665}{2*-9500}=\frac{0}{-19000}
=0
$