4x-5=2/3x+5

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

4x-5=2/3x+5

We move all terms to the left:

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


Domain of the equation: 3x+5)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-15x-15x-2=0

We add all the numbers together, and all the variables

12x^2-30x-2=0

a = 12; b = -30; c = -2;
Δ = b2-4ac
Δ = -302-4·12·(-2)
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{249}}{2*12}=\frac{30-2\sqrt{249}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{249}}{2*12}=\frac{30+2\sqrt{249}}{24}
$