8x+15=2/3x-3

Solution for 8x+15=2/3x-3 equation:

8x+15=2/3x-3

We move all terms to the left:

8x+15-(2/3x-3)=0


Domain of the equation: 3x-3)!=0

x∈R


We get rid of parentheses

8x-2/3x+3+15=0

We multiply all the terms by the denominator


8x*3x+3*3x+15*3x-2=0

Wy multiply elements

24x^2+9x+45x-2=0

We add all the numbers together, and all the variables

24x^2+54x-2=0

a = 24; b = 54; c = -2;
Δ = b2-4ac
Δ = 542-4·24·(-2)
Δ = 3108
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:

$\sqrt{\Delta}=\sqrt{3108}=\sqrt{4*777}=\sqrt{4}*\sqrt{777}=2\sqrt{777}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{777}}{2*24}=\frac{-54-2\sqrt{777}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{777}}{2*24}=\frac{-54+2\sqrt{777}}{48}
$