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4x^2-5x-44=9
We move all terms to the left:
4x^2-5x-44-(9)=0
We add all the numbers together, and all the variables
4x^2-5x-53=0
a = 4; b = -5; c = -53;
Δ = b2-4ac
Δ = -52-4·4·(-53)
Δ = 873
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{873}=\sqrt{9*97}=\sqrt{9}*\sqrt{97}=3\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{97}}{2*4}=\frac{5-3\sqrt{97}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{97}}{2*4}=\frac{5+3\sqrt{97}}{8} $
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