5/8x+7=x-11

Solution for 5/8x+7=x-11 equation:

5/8x+7=x-11

We move all terms to the left:

5/8x+7-(x-11)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

5/8x-x+11+7=0

We multiply all the terms by the denominator


-x*8x+11*8x+7*8x+5=0

Wy multiply elements

-8x^2+88x+56x+5=0

We add all the numbers together, and all the variables

-8x^2+144x+5=0

a = -8; b = 144; c = +5;
Δ = b2-4ac
Δ = 1442-4·(-8)·5
Δ = 20896
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:

$\sqrt{\Delta}=\sqrt{20896}=\sqrt{16*1306}=\sqrt{16}*\sqrt{1306}=4\sqrt{1306}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-4\sqrt{1306}}{2*-8}=\frac{-144-4\sqrt{1306}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+4\sqrt{1306}}{2*-8}=\frac{-144+4\sqrt{1306}}{-16}
$