8/3x+70=5x

Solution for 8/3x+70=5x equation:

8/3x+70=5x

We move all terms to the left:

8/3x+70-(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+8/3x+70=0

We multiply all the terms by the denominator


-5x*3x+70*3x+8=0

Wy multiply elements

-15x^2+210x+8=0

a = -15; b = 210; c = +8;
Δ = b2-4ac
Δ = 2102-4·(-15)·8
Δ = 44580
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:

$\sqrt{\Delta}=\sqrt{44580}=\sqrt{4*11145}=\sqrt{4}*\sqrt{11145}=2\sqrt{11145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(210)-2\sqrt{11145}}{2*-15}=\frac{-210-2\sqrt{11145}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(210)+2\sqrt{11145}}{2*-15}=\frac{-210+2\sqrt{11145}}{-30}
$