7/3x+8=5x

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

7/3x+8=5x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-15x^2+24x+7=0

a = -15; b = 24; c = +7;
Δ = b2-4ac
Δ = 242-4·(-15)·7
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{-(24)-2\sqrt{249}}{2*-15}=\frac{-24-2\sqrt{249}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{249}}{2*-15}=\frac{-24+2\sqrt{249}}{-30}
$