5x=(-30/7)

Solution for 5x=(-30/7) equation:

5x=(-30/7)

We move all terms to the left:

5x-((-30/7))=0

We multiply all the terms by the denominator


5x*7))-((-30=0

Wy multiply elements

35x^2-30=0

a = 35; b = 0; c = -30;
Δ = b2-4ac
Δ = 02-4·35·(-30)
Δ = 4200
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:

$\sqrt{\Delta}=\sqrt{4200}=\sqrt{100*42}=\sqrt{100}*\sqrt{42}=10\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{42}}{2*35}=\frac{0-10\sqrt{42}}{70}
=-\frac{10\sqrt{42}}{70}
=-\frac{\sqrt{42}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{42}}{2*35}=\frac{0+10\sqrt{42}}{70}
=\frac{10\sqrt{42}}{70}
=\frac{\sqrt{42}}{7}
$