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6x(-2x+5)=11
We move all terms to the left:
6x(-2x+5)-(11)=0
We multiply parentheses
-12x^2+30x-11=0
a = -12; b = 30; c = -11;
Δ = b2-4ac
Δ = 302-4·(-12)·(-11)
Δ = 372
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{93}}{2*-12}=\frac{-30-2\sqrt{93}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{93}}{2*-12}=\frac{-30+2\sqrt{93}}{-24} $
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