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42+3x(2x-7)+21x=642
We move all terms to the left:
42+3x(2x-7)+21x-(642)=0
We add all the numbers together, and all the variables
21x+3x(2x-7)-600=0
We multiply parentheses
6x^2+21x-21x-600=0
We add all the numbers together, and all the variables
6x^2-600=0
a = 6; b = 0; c = -600;
Δ = b2-4ac
Δ = 02-4·6·(-600)
Δ = 14400
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{14400}=120$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120}{2*6}=\frac{-120}{12} =-10 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120}{2*6}=\frac{120}{12} =10 $
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