3/5x-5x+60=7

Solution for 3/5x-5x+60=7 equation:

3/5x-5x+60=7

We move all terms to the left:

3/5x-5x+60-(7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-5x+3/5x+53=0

We multiply all the terms by the denominator


-5x*5x+53*5x+3=0

Wy multiply elements

-25x^2+265x+3=0

a = -25; b = 265; c = +3;
Δ = b2-4ac
Δ = 2652-4·(-25)·3
Δ = 70525
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:

$\sqrt{\Delta}=\sqrt{70525}=\sqrt{25*2821}=\sqrt{25}*\sqrt{2821}=5\sqrt{2821}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(265)-5\sqrt{2821}}{2*-25}=\frac{-265-5\sqrt{2821}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(265)+5\sqrt{2821}}{2*-25}=\frac{-265+5\sqrt{2821}}{-50}
$