2x+4x-8=3/510x+15

Solution for 2x+4x-8=3/510x+15 equation:

2x+4x-8=3/510x+15

We move all terms to the left:

2x+4x-8-(3/510x+15)=0


Domain of the equation: 510x+15)!=0

x∈R


We add all the numbers together, and all the variables

6x-(3/510x+15)-8=0

We get rid of parentheses

6x-3/510x-15-8=0

We multiply all the terms by the denominator


6x*510x-15*510x-8*510x-3=0

Wy multiply elements

3060x^2-7650x-4080x-3=0

We add all the numbers together, and all the variables

3060x^2-11730x-3=0

a = 3060; b = -11730; c = -3;
Δ = b2-4ac
Δ = -117302-4·3060·(-3)
Δ = 137629620
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:

$\sqrt{\Delta}=\sqrt{137629620}=\sqrt{36*3823045}=\sqrt{36}*\sqrt{3823045}=6\sqrt{3823045}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11730)-6\sqrt{3823045}}{2*3060}=\frac{11730-6\sqrt{3823045}}{6120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11730)+6\sqrt{3823045}}{2*3060}=\frac{11730+6\sqrt{3823045}}{6120}
$