-2/5x+3=1.5x+11

Solution for -2/5x+3=1.5x+11 equation:

-2/5x+3=1.5x+11

We move all terms to the left:

-2/5x+3-(1.5x+11)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

-2/5x-1.5x-11+3=0

We multiply all the terms by the denominator


-(1.5x)*5x-11*5x+3*5x-2=0

We add all the numbers together, and all the variables

-(+1.5x)*5x-11*5x+3*5x-2=0

We multiply parentheses

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

Wy multiply elements

-5x^2-55x+15x-2=0

We add all the numbers together, and all the variables

-5x^2-40x-2=0

a = -5; b = -40; c = -2;
Δ = b2-4ac
Δ = -402-4·(-5)·(-2)
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*-5}=\frac{40-2\sqrt{390}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{390}}{2*-5}=\frac{40+2\sqrt{390}}{-10}
$