5x^2-27=1-2x^2

Solution for 5x^2-27=1-2x^2 equation:

5x^2-27=1-2x^2

We move all terms to the left:

5x^2-27-(1-2x^2)=0

We get rid of parentheses

5x^2+2x^2-1-27=0

We add all the numbers together, and all the variables

7x^2-28=0

a = 7; b = 0; c = -28;
Δ = b2-4ac
Δ = 02-4·7·(-28)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28}{2*7}=\frac{-28}{14}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28}{2*7}=\frac{28}{14}
=2
$