-5x+3=-2/5x-20

Solution for -5x+3=-2/5x-20 equation:

-5x+3=-2/5x-20

We move all terms to the left:

-5x+3-(-2/5x-20)=0


Domain of the equation: 5x-20)!=0

x∈R


We get rid of parentheses

-5x+2/5x+20+3=0

We multiply all the terms by the denominator


-5x*5x+20*5x+3*5x+2=0

Wy multiply elements

-25x^2+100x+15x+2=0

We add all the numbers together, and all the variables

-25x^2+115x+2=0

a = -25; b = 115; c = +2;
Δ = b2-4ac
Δ = 1152-4·(-25)·2
Δ = 13425
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:

$\sqrt{\Delta}=\sqrt{13425}=\sqrt{25*537}=\sqrt{25}*\sqrt{537}=5\sqrt{537}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(115)-5\sqrt{537}}{2*-25}=\frac{-115-5\sqrt{537}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(115)+5\sqrt{537}}{2*-25}=\frac{-115+5\sqrt{537}}{-50}
$