4/5x+8=2x-3

Solution for 4/5x+8=2x-3 equation:

4/5x+8=2x-3

We move all terms to the left:

4/5x+8-(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+8=0

We multiply all the terms by the denominator


-2x*5x+3*5x+8*5x+4=0

Wy multiply elements

-10x^2+15x+40x+4=0

We add all the numbers together, and all the variables

-10x^2+55x+4=0

a = -10; b = 55; c = +4;
Δ = b2-4ac
Δ = 552-4·(-10)·4
Δ = 3185
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:

$\sqrt{\Delta}=\sqrt{3185}=\sqrt{49*65}=\sqrt{49}*\sqrt{65}=7\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-7\sqrt{65}}{2*-10}=\frac{-55-7\sqrt{65}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+7\sqrt{65}}{2*-10}=\frac{-55+7\sqrt{65}}{-20}
$