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x(-4x+21)=18
We move all terms to the left:
x(-4x+21)-(18)=0
We multiply parentheses
-4x^2+21x-18=0
a = -4; b = 21; c = -18;
Δ = b2-4ac
Δ = 212-4·(-4)·(-18)
Δ = 153
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{17}}{2*-4}=\frac{-21-3\sqrt{17}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{17}}{2*-4}=\frac{-21+3\sqrt{17}}{-8} $
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