.5x(4x-6)=11

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Solution for .5x(4x-6)=11 equation:



.5x(4x-6)=11
We move all terms to the left:
.5x(4x-6)-(11)=0
We multiply parentheses
4x^2-6x-11=0
a = 4; b = -6; c = -11;
Δ = b2-4ac
Δ = -62-4·4·(-11)
Δ = 212
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:
$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{53}}{2*4}=\frac{6-2\sqrt{53}}{8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{53}}{2*4}=\frac{6+2\sqrt{53}}{8} $

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