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-4x(2x-12)=28
We move all terms to the left:
-4x(2x-12)-(28)=0
We multiply parentheses
-8x^2+48x-28=0
a = -8; b = 48; c = -28;
Δ = b2-4ac
Δ = 482-4·(-8)·(-28)
Δ = 1408
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1408}=\sqrt{64*22}=\sqrt{64}*\sqrt{22}=8\sqrt{22}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{22}}{2*-8}=\frac{-48-8\sqrt{22}}{-16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{22}}{2*-8}=\frac{-48+8\sqrt{22}}{-16} $
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