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4x(6x-9.5)=46
We move all terms to the left:
4x(6x-9.5)-(46)=0
We multiply parentheses
24x^2-38x-46=0
a = 24; b = -38; c = -46;
Δ = b2-4ac
Δ = -382-4·24·(-46)
Δ = 5860
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5860}=\sqrt{4*1465}=\sqrt{4}*\sqrt{1465}=2\sqrt{1465}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{1465}}{2*24}=\frac{38-2\sqrt{1465}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{1465}}{2*24}=\frac{38+2\sqrt{1465}}{48} $
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