(3/x+1)(5x+5)=7

Solution for (3/x+1)(5x+5)=7 equation:

(3/x+1)(5x+5)=7

We move all terms to the left:

(3/x+1)(5x+5)-(7)=0


Domain of the equation: x+1)(5x+5)!=0

x∈R


We multiply parentheses ..

(+15x^2+15x+5x+5)-7=0

We get rid of parentheses

15x^2+15x+5x+5-7=0

We add all the numbers together, and all the variables

15x^2+20x-2=0

a = 15; b = 20; c = -2;
Δ = b2-4ac
Δ = 202-4·15·(-2)
Δ = 520
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:

$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{130}}{2*15}=\frac{-20-2\sqrt{130}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{130}}{2*15}=\frac{-20+2\sqrt{130}}{30}
$