12x+8=4/5(15x)-2

Solution for 12x+8=4/5(15x)-2 equation:

12x+8=4/5(15x)-2

We move all terms to the left:

12x+8-(4/5(15x)-2)=0


Domain of the equation: 515x-2)!=0

x∈R


We get rid of parentheses

12x-4/515x+2+8=0

We multiply all the terms by the denominator


12x*515x+2*515x+8*515x-4=0

Wy multiply elements

6180x^2+1030x+4120x-4=0

We add all the numbers together, and all the variables

6180x^2+5150x-4=0

a = 6180; b = 5150; c = -4;
Δ = b2-4ac
Δ = 51502-4·6180·(-4)
Δ = 26621380
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:

$\sqrt{\Delta}=\sqrt{26621380}=\sqrt{4*6655345}=\sqrt{4}*\sqrt{6655345}=2\sqrt{6655345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5150)-2\sqrt{6655345}}{2*6180}=\frac{-5150-2\sqrt{6655345}}{12360}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5150)+2\sqrt{6655345}}{2*6180}=\frac{-5150+2\sqrt{6655345}}{12360}
$