x^2*19/3=291

Solution for x^2*19/3=291 equation:

x^2*19/3=291

We move all terms to the left:

x^2*19/3-(291)=0

We multiply all the terms by the denominator


x^2*19-291*3=0

We add all the numbers together, and all the variables

x^2*19-873=0

Wy multiply elements

19x^2-873=0

a = 19; b = 0; c = -873;
Δ = b2-4ac
Δ = 02-4·19·(-873)
Δ = 66348
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:

$\sqrt{\Delta}=\sqrt{66348}=\sqrt{36*1843}=\sqrt{36}*\sqrt{1843}=6\sqrt{1843}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{1843}}{2*19}=\frac{0-6\sqrt{1843}}{38}
=-\frac{6\sqrt{1843}}{38}
=-\frac{3\sqrt{1843}}{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{1843}}{2*19}=\frac{0+6\sqrt{1843}}{38}
=\frac{6\sqrt{1843}}{38}
=\frac{3\sqrt{1843}}{19}
$