(3/4)(2x+8)=5-x

Solution for (3/4)(2x+8)=5-x equation:

(3/4)(2x+8)=5-x

We move all terms to the left:

(3/4)(2x+8)-(5-x)=0


Domain of the equation: 4)(2x+8)!=0

x∈R


We add all the numbers together, and all the variables

(+3/4)(2x+8)-(-1x+5)=0

We get rid of parentheses

(+3/4)(2x+8)+1x-5=0

We multiply parentheses ..

(+6x^2+3/4*8)+1x-5=0

We multiply all the terms by the denominator


(+6x^2+3+1x*4*8)-5*4*8)=0

We add all the numbers together, and all the variables

(+6x^2+3+1x*4*8)=0

We get rid of parentheses

6x^2+1x*4*8+3=0

Wy multiply elements

6x^2+32x*8+3=0

Wy multiply elements

6x^2+256x+3=0

a = 6; b = 256; c = +3;
Δ = b2-4ac
Δ = 2562-4·6·3
Δ = 65464
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:

$\sqrt{\Delta}=\sqrt{65464}=\sqrt{196*334}=\sqrt{196}*\sqrt{334}=14\sqrt{334}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(256)-14\sqrt{334}}{2*6}=\frac{-256-14\sqrt{334}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(256)+14\sqrt{334}}{2*6}=\frac{-256+14\sqrt{334}}{12}
$