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4x(x+12)-19=49
We move all terms to the left:
4x(x+12)-19-(49)=0
We add all the numbers together, and all the variables
4x(x+12)-68=0
We multiply parentheses
4x^2+48x-68=0
a = 4; b = 48; c = -68;
Δ = b2-4ac
Δ = 482-4·4·(-68)
Δ = 3392
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3392}=\sqrt{64*53}=\sqrt{64}*\sqrt{53}=8\sqrt{53}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{53}}{2*4}=\frac{-48-8\sqrt{53}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{53}}{2*4}=\frac{-48+8\sqrt{53}}{8} $
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