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7=5x^2-44x-9
We move all terms to the left:
7-(5x^2-44x-9)=0
We get rid of parentheses
-5x^2+44x+9+7=0
We add all the numbers together, and all the variables
-5x^2+44x+16=0
a = -5; b = 44; c = +16;
Δ = b2-4ac
Δ = 442-4·(-5)·16
Δ = 2256
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2256}=\sqrt{16*141}=\sqrt{16}*\sqrt{141}=4\sqrt{141}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{141}}{2*-5}=\frac{-44-4\sqrt{141}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{141}}{2*-5}=\frac{-44+4\sqrt{141}}{-10} $
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