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4x(6x+19)=13
We move all terms to the left:
4x(6x+19)-(13)=0
We multiply parentheses
24x^2+76x-13=0
a = 24; b = 76; c = -13;
Δ = b2-4ac
Δ = 762-4·24·(-13)
Δ = 7024
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7024}=\sqrt{16*439}=\sqrt{16}*\sqrt{439}=4\sqrt{439}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-4\sqrt{439}}{2*24}=\frac{-76-4\sqrt{439}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+4\sqrt{439}}{2*24}=\frac{-76+4\sqrt{439}}{48} $
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