3/5x+12=2x-3

Solution for 3/5x+12=2x-3 equation:

3/5x+12=2x-3

We move all terms to the left:

3/5x+12-(2x-3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x-2x+3+12=0

We multiply all the terms by the denominator


-2x*5x+3*5x+12*5x+3=0

Wy multiply elements

-10x^2+15x+60x+3=0

We add all the numbers together, and all the variables

-10x^2+75x+3=0

a = -10; b = 75; c = +3;
Δ = b2-4ac
Δ = 752-4·(-10)·3
Δ = 5745
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-\sqrt{5745}}{2*-10}=\frac{-75-\sqrt{5745}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+\sqrt{5745}}{2*-10}=\frac{-75+\sqrt{5745}}{-20}
$