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6x(4x-14)=25
We move all terms to the left:
6x(4x-14)-(25)=0
We multiply parentheses
24x^2-84x-25=0
a = 24; b = -84; c = -25;
Δ = b2-4ac
Δ = -842-4·24·(-25)
Δ = 9456
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9456}=\sqrt{16*591}=\sqrt{16}*\sqrt{591}=4\sqrt{591}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{591}}{2*24}=\frac{84-4\sqrt{591}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{591}}{2*24}=\frac{84+4\sqrt{591}}{48} $
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