-2/7x+3=2x+5

Solution for -2/7x+3=2x+5 equation:

-2/7x+3=2x+5

We move all terms to the left:

-2/7x+3-(2x+5)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

-2/7x-2x-5+3=0

We multiply all the terms by the denominator


-2x*7x-5*7x+3*7x-2=0

Wy multiply elements

-14x^2-35x+21x-2=0

We add all the numbers together, and all the variables

-14x^2-14x-2=0

a = -14; b = -14; c = -2;
Δ = b2-4ac
Δ = -142-4·(-14)·(-2)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{21}}{2*-14}=\frac{14-2\sqrt{21}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{21}}{2*-14}=\frac{14+2\sqrt{21}}{-28}
$