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0=-16x^2+120x+7
We move all terms to the left:
0-(-16x^2+120x+7)=0
We add all the numbers together, and all the variables
-(-16x^2+120x+7)=0
We get rid of parentheses
16x^2-120x-7=0
a = 16; b = -120; c = -7;
Δ = b2-4ac
Δ = -1202-4·16·(-7)
Δ = 14848
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14848}=\sqrt{256*58}=\sqrt{256}*\sqrt{58}=16\sqrt{58}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-16\sqrt{58}}{2*16}=\frac{120-16\sqrt{58}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+16\sqrt{58}}{2*16}=\frac{120+16\sqrt{58}}{32} $
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