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-4x^2-7x-9x=2
We move all terms to the left:
-4x^2-7x-9x-(2)=0
We add all the numbers together, and all the variables
-4x^2-16x-2=0
a = -4; b = -16; c = -2;
Δ = b2-4ac
Δ = -162-4·(-4)·(-2)
Δ = 224
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{14}}{2*-4}=\frac{16-4\sqrt{14}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{14}}{2*-4}=\frac{16+4\sqrt{14}}{-8} $
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