8x+5=10/3x-7

Solution for 8x+5=10/3x-7 equation:

8x+5=10/3x-7

We move all terms to the left:

8x+5-(10/3x-7)=0


Domain of the equation: 3x-7)!=0

x∈R


We get rid of parentheses

8x-10/3x+7+5=0

We multiply all the terms by the denominator


8x*3x+7*3x+5*3x-10=0

Wy multiply elements

24x^2+21x+15x-10=0

We add all the numbers together, and all the variables

24x^2+36x-10=0

a = 24; b = 36; c = -10;
Δ = b2-4ac
Δ = 362-4·24·(-10)
Δ = 2256
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:

$\sqrt{\Delta}=\sqrt{2256}=\sqrt{16*141}=\sqrt{16}*\sqrt{141}=4\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{141}}{2*24}=\frac{-36-4\sqrt{141}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{141}}{2*24}=\frac{-36+4\sqrt{141}}{48}
$