5u+7=5/2u-1

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

5u+7=5/2u-1

We move all terms to the left:

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


Domain of the equation: 2u-1)!=0

u∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


5u*2u+1*2u+7*2u-5=0

Wy multiply elements

10u^2+2u+14u-5=0

We add all the numbers together, and all the variables

10u^2+16u-5=0

a = 10; b = 16; c = -5;
Δ = b2-4ac
Δ = 162-4·10·(-5)
Δ = 456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{114}}{2*10}=\frac{-16-2\sqrt{114}}{20}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{114}}{2*10}=\frac{-16+2\sqrt{114}}{20}
$