5x=(-53/5)

Solution for 5x=(-53/5) equation:

5x=(-53/5)

We move all terms to the left:

5x-((-53/5))=0

We multiply all the terms by the denominator


5x*5))-((-53=0

Wy multiply elements

25x^2-53=0

a = 25; b = 0; c = -53;
Δ = b2-4ac
Δ = 02-4·25·(-53)
Δ = 5300
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:

$\sqrt{\Delta}=\sqrt{5300}=\sqrt{100*53}=\sqrt{100}*\sqrt{53}=10\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{53}}{2*25}=\frac{0-10\sqrt{53}}{50}
=-\frac{10\sqrt{53}}{50}
=-\frac{\sqrt{53}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{53}}{2*25}=\frac{0+10\sqrt{53}}{50}
=\frac{10\sqrt{53}}{50}
=\frac{\sqrt{53}}{5}
$