9/10*u-3/4=2/3*u-5

Solution for 9/10*u-3/4=2/3*u-5 equation:

9/10u-3/4=2/3u-5

We move all terms to the left:

9/10u-3/4-(2/3u-5)=0


Domain of the equation: 10u!=0

u!=0/10

u!=0

u∈R



Domain of the equation: 3u-5)!=0

u∈R


We get rid of parentheses

9/10u-2/3u+5-3/4=0

We calculate fractions


(-270u^2)/480u^2+432u/480u^2+(-320u)/480u^2+5=0

We multiply all the terms by the denominator


(-270u^2)+432u+(-320u)+5*480u^2=0

Wy multiply elements

(-270u^2)+2400u^2+432u+(-320u)=0

We get rid of parentheses

-270u^2+2400u^2+432u-320u=0

We add all the numbers together, and all the variables

2130u^2+112u=0

a = 2130; b = 112; c = 0;
Δ = b2-4ac
Δ = 1122-4·2130·0
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*2130}=\frac{-224}{4260}
=-56/1065
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+112}{2*2130}=\frac{0}{4260}
=0
$