x^2+14/5=27

Solution for x^2+14/5=27 equation:

x^2+14/5=27

We move all terms to the left:

x^2+14/5-(27)=0

determiningTheFunctionDomain
x^2-27+14/5=0

We multiply all the terms by the denominator


x^2*5+14-27*5=0

We add all the numbers together, and all the variables

x^2*5-121=0

Wy multiply elements

5x^2-121=0

a = 5; b = 0; c = -121;
Δ = b2-4ac
Δ = 02-4·5·(-121)
Δ = 2420
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:

$\sqrt{\Delta}=\sqrt{2420}=\sqrt{484*5}=\sqrt{484}*\sqrt{5}=22\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22\sqrt{5}}{2*5}=\frac{0-22\sqrt{5}}{10}
=-\frac{22\sqrt{5}}{10}
=-\frac{11\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{5}}{2*5}=\frac{0+22\sqrt{5}}{10}
=\frac{22\sqrt{5}}{10}
=\frac{11\sqrt{5}}{5}
$