(1/3)(4x+5)=8x

Solution for (1/3)(4x+5)=8x equation:

(1/3)(4x+5)=8x

We move all terms to the left:

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


Domain of the equation: 3)(4x+5)!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


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

We get rid of parentheses

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

Wy multiply elements

4x^2-120x*5+1=0

Wy multiply elements

4x^2-600x+1=0

a = 4; b = -600; c = +1;
Δ = b2-4ac
Δ = -6002-4·4·1
Δ = 359984
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:

$\sqrt{\Delta}=\sqrt{359984}=\sqrt{16*22499}=\sqrt{16}*\sqrt{22499}=4\sqrt{22499}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-4\sqrt{22499}}{2*4}=\frac{600-4\sqrt{22499}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+4\sqrt{22499}}{2*4}=\frac{600+4\sqrt{22499}}{8}
$