-61/2x-2=24-8.5x

Solution for -61/2x-2=24-8.5x equation:

-61/2x-2=24-8.5x

We move all terms to the left:

-61/2x-2-(24-8.5x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-61/2x-(-8.5x+24)-2=0

We get rid of parentheses

-61/2x+8.5x-24-2=0

We multiply all the terms by the denominator


(8.5x)*2x-24*2x-2*2x-61=0

We add all the numbers together, and all the variables

(+8.5x)*2x-24*2x-2*2x-61=0

We multiply parentheses

16x^2-24*2x-2*2x-61=0

Wy multiply elements

16x^2-48x-4x-61=0

We add all the numbers together, and all the variables

16x^2-52x-61=0

a = 16; b = -52; c = -61;
Δ = b2-4ac
Δ = -522-4·16·(-61)
Δ = 6608
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:

$\sqrt{\Delta}=\sqrt{6608}=\sqrt{16*413}=\sqrt{16}*\sqrt{413}=4\sqrt{413}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{413}}{2*16}=\frac{52-4\sqrt{413}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{413}}{2*16}=\frac{52+4\sqrt{413}}{32}
$