2x+2=3x-6/52x+2=3x-6/5

Solution for 2x+2=3x-6/52x+2=3x-6/5 equation:

2x+2=3x-6/52x+2=3x-6/5

We move all terms to the left:

2x+2-(3x-6/52x+2)=0


Domain of the equation: 52x+2)!=0

x∈R


We get rid of parentheses

2x-3x+6/52x-2+2=0

We multiply all the terms by the denominator


2x*52x-3x*52x-2*52x+2*52x+6=0

Wy multiply elements

104x^2-156x^2-104x+104x+6=0

We add all the numbers together, and all the variables

-52x^2+6=0

a = -52; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-52)·6
Δ = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{78}}{2*-52}=\frac{0-4\sqrt{78}}{-104}
=-\frac{4\sqrt{78}}{-104}
=-\frac{\sqrt{78}}{-26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{78}}{2*-52}=\frac{0+4\sqrt{78}}{-104}
=\frac{4\sqrt{78}}{-104}
=\frac{\sqrt{78}}{-26}
$