x*x=4+17/18

Solution for x*x=4+17/18 equation:

x*x=4+17/18

We move all terms to the left:

x*x-(4+17/18)=0

We add all the numbers together, and all the variables

x*x-(17/18+4)=0

Wy multiply elements

x^2-(17/18+4)=0

We get rid of parentheses

x^2-4-17/18=0

We multiply all the terms by the denominator


x^2*18-17-4*18=0

We add all the numbers together, and all the variables

x^2*18-89=0

Wy multiply elements

18x^2-89=0

a = 18; b = 0; c = -89;
Δ = b2-4ac
Δ = 02-4·18·(-89)
Δ = 6408
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:

$\sqrt{\Delta}=\sqrt{6408}=\sqrt{36*178}=\sqrt{36}*\sqrt{178}=6\sqrt{178}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{178}}{2*18}=\frac{0-6\sqrt{178}}{36}
=-\frac{6\sqrt{178}}{36}
=-\frac{\sqrt{178}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{178}}{2*18}=\frac{0+6\sqrt{178}}{36}
=\frac{6\sqrt{178}}{36}
=\frac{\sqrt{178}}{6}
$