6/5x+7=2x-4

Solution for 6/5x+7=2x-4 equation:

6/5x+7=2x-4

We move all terms to the left:

6/5x+7-(2x-4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

6/5x-2x+4+7=0

We multiply all the terms by the denominator


-2x*5x+4*5x+7*5x+6=0

Wy multiply elements

-10x^2+20x+35x+6=0

We add all the numbers together, and all the variables

-10x^2+55x+6=0

a = -10; b = 55; c = +6;
Δ = b2-4ac
Δ = 552-4·(-10)·6
Δ = 3265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-\sqrt{3265}}{2*-10}=\frac{-55-\sqrt{3265}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{3265}}{2*-10}=\frac{-55+\sqrt{3265}}{-20}
$