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

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

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

We move all terms to the left:

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


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

x∈R



Domain of the equation: 8x-2))!=0

x∈R


We multiply parentheses

12x-(4(5/8x-2))+20=0

We multiply all the terms by the denominator


12x*8x+20*8x-2))-(4(5-2))=0

We add all the numbers together, and all the variables

12x*8x+20*8x-2))-(43)=0

We add all the numbers together, and all the variables

12x*8x+20*8x=0

Wy multiply elements

96x^2+160x=0

a = 96; b = 160; c = 0;
Δ = b2-4ac
Δ = 1602-4·96·0
Δ = 25600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25600}=160$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-160}{2*96}=\frac{-320}{192}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+160}{2*96}=\frac{0}{192}
=0
$