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(14-x)x-2=-50
We move all terms to the left:
(14-x)x-2-(-50)=0
We add all the numbers together, and all the variables
(-1x+14)x-2-(-50)=0
We add all the numbers together, and all the variables
(-1x+14)x+48=0
We multiply parentheses
-1x^2+14x+48=0
a = -1; b = 14; c = +48;
Δ = b2-4ac
Δ = 142-4·(-1)·48
Δ = 388
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{97}}{2*-1}=\frac{-14-2\sqrt{97}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{97}}{2*-1}=\frac{-14+2\sqrt{97}}{-2} $
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