4/3x-7=5x-13

Solution for 4/3x-7=5x-13 equation:

4/3x-7=5x-13

We move all terms to the left:

4/3x-7-(5x-13)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

4/3x-5x+13-7=0

We multiply all the terms by the denominator


-5x*3x+13*3x-7*3x+4=0

Wy multiply elements

-15x^2+39x-21x+4=0

We add all the numbers together, and all the variables

-15x^2+18x+4=0

a = -15; b = 18; c = +4;
Δ = b2-4ac
Δ = 182-4·(-15)·4
Δ = 564
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:

$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{141}}{2*-15}=\frac{-18-2\sqrt{141}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{141}}{2*-15}=\frac{-18+2\sqrt{141}}{-30}
$