4/5x+8=29+20x

Solution for 4/5x+8=29+20x equation:

4/5x+8=29+20x

We move all terms to the left:

4/5x+8-(29+20x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

4/5x-(20x+29)+8=0

We get rid of parentheses

4/5x-20x-29+8=0

We multiply all the terms by the denominator


-20x*5x-29*5x+8*5x+4=0

Wy multiply elements

-100x^2-145x+40x+4=0

We add all the numbers together, and all the variables

-100x^2-105x+4=0

a = -100; b = -105; c = +4;
Δ = b2-4ac
Δ = -1052-4·(-100)·4
Δ = 12625
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:

$\sqrt{\Delta}=\sqrt{12625}=\sqrt{25*505}=\sqrt{25}*\sqrt{505}=5\sqrt{505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-5\sqrt{505}}{2*-100}=\frac{105-5\sqrt{505}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+5\sqrt{505}}{2*-100}=\frac{105+5\sqrt{505}}{-200}
$