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4x^2-12x=19
We move all terms to the left:
4x^2-12x-(19)=0
a = 4; b = -12; c = -19;
Δ = b2-4ac
Δ = -122-4·4·(-19)
Δ = 448
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{7}}{2*4}=\frac{12-8\sqrt{7}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{7}}{2*4}=\frac{12+8\sqrt{7}}{8} $
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