X^2+7=-4x^2-9x+4

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Solution for X^2+7=-4x^2-9x+4 equation:



X^2+7=-4X^2-9X+4
We move all terms to the left:
X^2+7-(-4X^2-9X+4)=0
We get rid of parentheses
X^2+4X^2+9X-4+7=0
We add all the numbers together, and all the variables
5X^2+9X+3=0
a = 5; b = 9; c = +3;
Δ = b2-4ac
Δ = 92-4·5·3
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{21}}{2*5}=\frac{-9-\sqrt{21}}{10} $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{21}}{2*5}=\frac{-9+\sqrt{21}}{10} $

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