1/2x+14=2.5x-4

Solution for 1/2x+14=2.5x-4 equation:

1/2x+14=2.5x-4

We move all terms to the left:

1/2x+14-(2.5x-4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-2.5x+4+14=0

We multiply all the terms by the denominator


-(2.5x)*2x+4*2x+14*2x+1=0

We add all the numbers together, and all the variables

-(+2.5x)*2x+4*2x+14*2x+1=0

We multiply parentheses

-4x^2+4*2x+14*2x+1=0

Wy multiply elements

-4x^2+8x+28x+1=0

We add all the numbers together, and all the variables

-4x^2+36x+1=0

a = -4; b = 36; c = +1;
Δ = b2-4ac
Δ = 362-4·(-4)·1
Δ = 1312
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:

$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{82}}{2*-4}=\frac{-36-4\sqrt{82}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{82}}{2*-4}=\frac{-36+4\sqrt{82}}{-8}
$