2/5x-3=2x-11

Solution for 2/5x-3=2x-11 equation:

2/5x-3=2x-11

We move all terms to the left:

2/5x-3-(2x-11)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x-2x+11-3=0

We multiply all the terms by the denominator


-2x*5x+11*5x-3*5x+2=0

Wy multiply elements

-10x^2+55x-15x+2=0

We add all the numbers together, and all the variables

-10x^2+40x+2=0

a = -10; b = 40; c = +2;
Δ = b2-4ac
Δ = 402-4·(-10)·2
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{105}}{2*-10}=\frac{-40-4\sqrt{105}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{105}}{2*-10}=\frac{-40+4\sqrt{105}}{-20}
$