5x=(-10/3)

Solution for 5x=(-10/3) equation:

5x=(-10/3)

We move all terms to the left:

5x-((-10/3))=0

We multiply all the terms by the denominator


5x*3))-((-10=0

Wy multiply elements

15x^2-10=0

a = 15; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·15·(-10)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*15}=\frac{0-10\sqrt{6}}{30}
=-\frac{10\sqrt{6}}{30}
=-\frac{\sqrt{6}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*15}=\frac{0+10\sqrt{6}}{30}
=\frac{10\sqrt{6}}{30}
=\frac{\sqrt{6}}{3}
$