7(2u+1)-(10u*2-15u)/(5u)=82

Solution for 7(2u+1)-(10u*2-15u)/(5u)=82 equation:

7(2u+1)-(10u*2-15u)/(5u)=82

We move all terms to the left:

7(2u+1)-(10u*2-15u)/(5u)-(82)=0


Domain of the equation: 5u!=0

u!=0/5

u!=0

u∈R


We add all the numbers together, and all the variables

7(2u+1)-(-15u+10u*2)/5u-82=0

We multiply parentheses

14u-(-15u+10u*2)/5u+7-82=0

We multiply all the terms by the denominator


14u*5u-(-15u+10u*2)+7*5u-82*5u=0

Wy multiply elements

70u^2-(-15u+10u*2)+35u-410u=0

We get rid of parentheses

70u^2+15u-10u*2+35u-410u=0

We add all the numbers together, and all the variables

70u^2-360u-10u*2=0

Wy multiply elements

70u^2-360u-20u=0

We add all the numbers together, and all the variables

70u^2-380u=0

a = 70; b = -380; c = 0;
Δ = b2-4ac
Δ = -3802-4·70·0
Δ = 144400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144400}=380$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-380)-380}{2*70}=\frac{0}{140}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-380)+380}{2*70}=\frac{760}{140}
=5+3/7
$