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63x(13-17x)-6x=63
We move all terms to the left:
63x(13-17x)-6x-(63)=0
We add all the numbers together, and all the variables
63x(-17x+13)-6x-63=0
We add all the numbers together, and all the variables
-6x+63x(-17x+13)-63=0
We multiply parentheses
-1071x^2-6x+819x-63=0
We add all the numbers together, and all the variables
-1071x^2+813x-63=0
a = -1071; b = 813; c = -63;
Δ = b2-4ac
Δ = 8132-4·(-1071)·(-63)
Δ = 391077
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{391077}=\sqrt{9*43453}=\sqrt{9}*\sqrt{43453}=3\sqrt{43453}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(813)-3\sqrt{43453}}{2*-1071}=\frac{-813-3\sqrt{43453}}{-2142} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(813)+3\sqrt{43453}}{2*-1071}=\frac{-813+3\sqrt{43453}}{-2142} $
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