5(3/5x-3)=3/4x-15

Solution for 5(3/5x-3)=3/4x-15 equation:

5(3/5x-3)=3/4x-15

We move all terms to the left:

5(3/5x-3)-(3/4x-15)=0


Domain of the equation: 5x-3)!=0

x∈R



Domain of the equation: 4x-15)!=0

x∈R


We multiply parentheses

15x-(3/4x-15)-15=0

We get rid of parentheses

15x-3/4x+15-15=0

We multiply all the terms by the denominator


15x*4x+15*4x-15*4x-3=0

Wy multiply elements

60x^2+60x-60x-3=0

We add all the numbers together, and all the variables

60x^2-3=0

a = 60; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·60·(-3)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*60}=\frac{0-12\sqrt{5}}{120}
=-\frac{12\sqrt{5}}{120}
=-\frac{\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*60}=\frac{0+12\sqrt{5}}{120}
=\frac{12\sqrt{5}}{120}
=\frac{\sqrt{5}}{10}
$