3/5x+16=-5x-7

Solution for 3/5x+16=-5x-7 equation:

3/5x+16=-5x-7

We move all terms to the left:

3/5x+16-(-5x-7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x+5x+7+16=0

We multiply all the terms by the denominator


5x*5x+7*5x+16*5x+3=0

Wy multiply elements

25x^2+35x+80x+3=0

We add all the numbers together, and all the variables

25x^2+115x+3=0

a = 25; b = 115; c = +3;
Δ = b2-4ac
Δ = 1152-4·25·3
Δ = 12925
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12925}=\sqrt{25*517}=\sqrt{25}*\sqrt{517}=5\sqrt{517}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(115)-5\sqrt{517}}{2*25}=\frac{-115-5\sqrt{517}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(115)+5\sqrt{517}}{2*25}=\frac{-115+5\sqrt{517}}{50}
$