5x2-27=2x2+48

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Solution for 5x2-27=2x2+48 equation:



5x^2-27=2x^2+48
We move all terms to the left:
5x^2-27-(2x^2+48)=0
We get rid of parentheses
5x^2-2x^2-48-27=0
We add all the numbers together, and all the variables
3x^2-75=0
a = 3; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·3·(-75)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30}{2*3}=\frac{-30}{6} =-5 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*3}=\frac{30}{6} =5 $

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