-5/6u-5/3=1/2u+7

Solution for -5/6u-5/3=1/2u+7 equation:

-5/6u-5/3=1/2u+7

We move all terms to the left:

-5/6u-5/3-(1/2u+7)=0


Domain of the equation: 6u!=0

u!=0/6

u!=0

u∈R



Domain of the equation: 2u+7)!=0

u∈R


We get rid of parentheses

-5/6u-1/2u-7-5/3=0

We calculate fractions


(-120u^2)/108u^2+(-90u)/108u^2+(-54u)/108u^2-7=0

We multiply all the terms by the denominator


(-120u^2)+(-90u)+(-54u)-7*108u^2=0

Wy multiply elements

(-120u^2)-756u^2+(-90u)+(-54u)=0

We get rid of parentheses

-120u^2-756u^2-90u-54u=0

We add all the numbers together, and all the variables

-876u^2-144u=0

a = -876; b = -144; c = 0;
Δ = b2-4ac
Δ = -1442-4·(-876)·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-144}{2*-876}=\frac{0}{-1752}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+144}{2*-876}=\frac{288}{-1752}
=-12/73
$