(5)/(2)x+8-12x=16-15x

Solution for (5)/(2)x+8-12x=16-15x equation:

(5)/(2)x+8-12x=16-15x

We move all terms to the left:

(5)/(2)x+8-12x-(16-15x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x-12x-(-15x+16)+8=0

We add all the numbers together, and all the variables

-12x+5/2x-(-15x+16)+8=0

We get rid of parentheses

-12x+5/2x+15x-16+8=0

We multiply all the terms by the denominator


-12x*2x+15x*2x-16*2x+8*2x+5=0

Wy multiply elements

-24x^2+30x^2-32x+16x+5=0

We add all the numbers together, and all the variables

6x^2-16x+5=0

a = 6; b = -16; c = +5;
Δ = b2-4ac
Δ = -162-4·6·5
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{34}}{2*6}=\frac{16-2\sqrt{34}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{34}}{2*6}=\frac{16+2\sqrt{34}}{12}
$