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3x(3x+x+4)=8(8+19)
We move all terms to the left:
3x(3x+x+4)-(8(8+19))=0
We add all the numbers together, and all the variables
3x(4x+4)-(827)=0
We add all the numbers together, and all the variables
3x(4x+4)-827=0
We multiply parentheses
12x^2+12x-827=0
a = 12; b = 12; c = -827;
Δ = b2-4ac
Δ = 122-4·12·(-827)
Δ = 39840
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{39840}=\sqrt{16*2490}=\sqrt{16}*\sqrt{2490}=4\sqrt{2490}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{2490}}{2*12}=\frac{-12-4\sqrt{2490}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{2490}}{2*12}=\frac{-12+4\sqrt{2490}}{24} $
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