4/5x+5=2x-3

Solution for 4/5x+5=2x-3 equation:

4/5x+5=2x-3

We move all terms to the left:

4/5x+5-(2x-3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-2x+3+5=0

We multiply all the terms by the denominator


-2x*5x+3*5x+5*5x+4=0

Wy multiply elements

-10x^2+15x+25x+4=0

We add all the numbers together, and all the variables

-10x^2+40x+4=0

a = -10; b = 40; c = +4;
Δ = b2-4ac
Δ = 402-4·(-10)·4
Δ = 1760
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:

$\sqrt{\Delta}=\sqrt{1760}=\sqrt{16*110}=\sqrt{16}*\sqrt{110}=4\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{110}}{2*-10}=\frac{-40-4\sqrt{110}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{110}}{2*-10}=\frac{-40+4\sqrt{110}}{-20}
$