3x+65=-7/5x-145

Solution for 3x+65=-7/5x-145 equation:

3x+65=-7/5x-145

We move all terms to the left:

3x+65-(-7/5x-145)=0


Domain of the equation: 5x-145)!=0

x∈R


We get rid of parentheses

3x+7/5x+145+65=0

We multiply all the terms by the denominator


3x*5x+145*5x+65*5x+7=0

Wy multiply elements

15x^2+725x+325x+7=0

We add all the numbers together, and all the variables

15x^2+1050x+7=0

a = 15; b = 1050; c = +7;
Δ = b2-4ac
Δ = 10502-4·15·7
Δ = 1102080
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:

$\sqrt{\Delta}=\sqrt{1102080}=\sqrt{256*4305}=\sqrt{256}*\sqrt{4305}=16\sqrt{4305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1050)-16\sqrt{4305}}{2*15}=\frac{-1050-16\sqrt{4305}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1050)+16\sqrt{4305}}{2*15}=\frac{-1050+16\sqrt{4305}}{30}
$