x=3(-31/19)+7

Solution for x=3(-31/19)+7 equation:

x=3(-31/19)+7

We move all terms to the left:

x-(3(-31/19)+7)=0

We multiply all the terms by the denominator


x*19)+7)-(3(-31=0

Wy multiply elements

19x^2-31=0

a = 19; b = 0; c = -31;
Δ = b2-4ac
Δ = 02-4·19·(-31)
Δ = 2356
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:

$\sqrt{\Delta}=\sqrt{2356}=\sqrt{4*589}=\sqrt{4}*\sqrt{589}=2\sqrt{589}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{589}}{2*19}=\frac{0-2\sqrt{589}}{38}
=-\frac{2\sqrt{589}}{38}
=-\frac{\sqrt{589}}{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{589}}{2*19}=\frac{0+2\sqrt{589}}{38}
=\frac{2\sqrt{589}}{38}
=\frac{\sqrt{589}}{19}
$