4/5x-13=8-3x

Solution for 4/5x-13=8-3x equation:

4/5x-13=8-3x

We move all terms to the left:

4/5x-13-(8-3x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

4/5x-(-3x+8)-13=0

We get rid of parentheses

4/5x+3x-8-13=0

We multiply all the terms by the denominator


3x*5x-8*5x-13*5x+4=0

Wy multiply elements

15x^2-40x-65x+4=0

We add all the numbers together, and all the variables

15x^2-105x+4=0

a = 15; b = -105; c = +4;
Δ = b2-4ac
Δ = -1052-4·15·4
Δ = 10785
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-\sqrt{10785}}{2*15}=\frac{105-\sqrt{10785}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{10785}}{2*15}=\frac{105+\sqrt{10785}}{30}
$