2.5(x+6)-3=5/2x+12

Solution for 2.5(x+6)-3=5/2x+12 equation:

2.5(x+6)-3=5/2x+12

We move all terms to the left:

2.5(x+6)-3-(5/2x+12)=0


Domain of the equation: 2x+12)!=0

x∈R


We multiply parentheses

2.5x-(5/2x+12)+15-3=0

We get rid of parentheses

2.5x-5/2x-12+15-3=0

We multiply all the terms by the denominator


(2.5x)*2x-12*2x+15*2x-3*2x-5=0

We add all the numbers together, and all the variables

(+2.5x)*2x-12*2x+15*2x-3*2x-5=0

We multiply parentheses

4x^2-12*2x+15*2x-3*2x-5=0

Wy multiply elements

4x^2-24x+30x-6x-5=0

We add all the numbers together, and all the variables

4x^2-5=0

a = 4; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·4·(-5)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*4}=\frac{0-4\sqrt{5}}{8}
=-\frac{4\sqrt{5}}{8}
=-\frac{\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*4}=\frac{0+4\sqrt{5}}{8}
=\frac{4\sqrt{5}}{8}
=\frac{\sqrt{5}}{2}
$