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

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

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

We move all terms to the left:

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


Domain of the equation: 2u!=0

u!=0/2

u!=0

u∈R



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

u∈R


We get rid of parentheses

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

We calculate fractions


(-875u)/250u^2+12u/250u^2+2u/250u^2+6=0

We multiply all the terms by the denominator


(-875u)+12u+2u+6*250u^2=0

We add all the numbers together, and all the variables

14u+(-875u)+6*250u^2=0

Wy multiply elements

1500u^2+14u+(-875u)=0

We get rid of parentheses

1500u^2+14u-875u=0

We add all the numbers together, and all the variables

1500u^2-861u=0

a = 1500; b = -861; c = 0;
Δ = b2-4ac
Δ = -8612-4·1500·0
Δ = 741321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{741321}=861$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-861)-861}{2*1500}=\frac{0}{3000}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-861)+861}{2*1500}=\frac{1722}{3000}
=287/500
$