-2x+3=1/5x+11

Solution for -2x+3=1/5x+11 equation:

-2x+3=1/5x+11

We move all terms to the left:

-2x+3-(1/5x+11)=0


Domain of the equation: 5x+11)!=0

x∈R


We get rid of parentheses

-2x-1/5x-11+3=0

We multiply all the terms by the denominator


-2x*5x-11*5x+3*5x-1=0

Wy multiply elements

-10x^2-55x+15x-1=0

We add all the numbers together, and all the variables

-10x^2-40x-1=0

a = -10; b = -40; c = -1;
Δ = b2-4ac
Δ = -402-4·(-10)·(-1)
Δ = 1560
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:

$\sqrt{\Delta}=\sqrt{1560}=\sqrt{4*390}=\sqrt{4}*\sqrt{390}=2\sqrt{390}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{390}}{2*-10}=\frac{40-2\sqrt{390}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{390}}{2*-10}=\frac{40+2\sqrt{390}}{-20}
$