x-11=5/8x+7

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

x-11=5/8x+7

We move all terms to the left:

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


Domain of the equation: 8x+7)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

8x^2-56x-88x-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}
$