2/5x+4=2.5x-12

Solution for 2/5x+4=2.5x-12 equation:

2/5x+4=2.5x-12

We move all terms to the left:

2/5x+4-(2.5x-12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x-2.5x+12+4=0

We multiply all the terms by the denominator


-(2.5x)*5x+12*5x+4*5x+2=0

We add all the numbers together, and all the variables

-(+2.5x)*5x+12*5x+4*5x+2=0

We multiply parentheses

-10x^2+12*5x+4*5x+2=0

Wy multiply elements

-10x^2+60x+20x+2=0

We add all the numbers together, and all the variables

-10x^2+80x+2=0

a = -10; b = 80; c = +2;
Δ = b2-4ac
Δ = 802-4·(-10)·2
Δ = 6480
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:

$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-36\sqrt{5}}{2*-10}=\frac{-80-36\sqrt{5}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+36\sqrt{5}}{2*-10}=\frac{-80+36\sqrt{5}}{-20}
$