3/5u-1/4=5/6u-5

Solution for 3/5u-1/4=5/6u-5 equation:

3/5u-1/4=5/6u-5

We move all terms to the left:

3/5u-1/4-(5/6u-5)=0


Domain of the equation: 5u!=0

u!=0/5

u!=0

u∈R



Domain of the equation: 6u-5)!=0

u∈R


We get rid of parentheses

3/5u-5/6u+5-1/4=0

We calculate fractions


(-180u^2)/480u^2+288u/480u^2+(-400u)/480u^2+5=0

We multiply all the terms by the denominator


(-180u^2)+288u+(-400u)+5*480u^2=0

Wy multiply elements

(-180u^2)+2400u^2+288u+(-400u)=0

We get rid of parentheses

-180u^2+2400u^2+288u-400u=0

We add all the numbers together, and all the variables

2220u^2-112u=0

a = 2220; b = -112; c = 0;
Δ = b2-4ac
Δ = -1122-4·2220·0
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-112}{2*2220}=\frac{0}{4440}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+112}{2*2220}=\frac{224}{4440}
=28/555
$