X*y=67/4(5)

Solution for X*y=67/4(5) equation:

X*X=67/4(5)

We move all terms to the left:

X*X-(67/4(5))=0

We add all the numbers together, and all the variables

X*X-(+67/45)=0

Wy multiply elements

X^2-(+67/45)=0

We get rid of parentheses

X^2-67/45=0

We multiply all the terms by the denominator


X^2*45-67=0

Wy multiply elements

45X^2-67=0

a = 45; b = 0; c = -67;
Δ = b2-4ac
Δ = 02-4·45·(-67)
Δ = 12060
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:

$\sqrt{\Delta}=\sqrt{12060}=\sqrt{36*335}=\sqrt{36}*\sqrt{335}=6\sqrt{335}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{335}}{2*45}=\frac{0-6\sqrt{335}}{90}
=-\frac{6\sqrt{335}}{90}
=-\frac{\sqrt{335}}{15}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{335}}{2*45}=\frac{0+6\sqrt{335}}{90}
=\frac{6\sqrt{335}}{90}
=\frac{\sqrt{335}}{15}
$