5/8x+6=28-x

Solution for 5/8x+6=28-x equation:

5/8x+6=28-x

We move all terms to the left:

5/8x+6-(28-x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

5/8x-(-1x+28)+6=0

We get rid of parentheses

5/8x+1x-28+6=0

We multiply all the terms by the denominator


1x*8x-28*8x+6*8x+5=0

Wy multiply elements

8x^2-224x+48x+5=0

We add all the numbers together, and all the variables

8x^2-176x+5=0

a = 8; b = -176; c = +5;
Δ = b2-4ac
Δ = -1762-4·8·5
Δ = 30816
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:

$\sqrt{\Delta}=\sqrt{30816}=\sqrt{144*214}=\sqrt{144}*\sqrt{214}=12\sqrt{214}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-176)-12\sqrt{214}}{2*8}=\frac{176-12\sqrt{214}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-176)+12\sqrt{214}}{2*8}=\frac{176+12\sqrt{214}}{16}
$