Solve x (2x-21)=180

Evaluate

x (2 x - 21) = 180

Expand the expression

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2 x^{2} - 21 x = 180

Move the expression to the left side

2 x^{2} - 21 x - 180 = 0

Substitute a= 2,b= - 21 and c= - 180 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{21 \pm ( - 21 ) ^{2} - 4 \times 2 ( - 180 )}{2 \times 2}

Simplify the expression

x = \frac{21 \pm ( - 21 ) ^{2} - 4 \times 2 ( - 180 )}{4}

Simplify the expression

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x = \frac{21 \pm 1881}{4}

Simplify the radical expression

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x = \frac{21 \pm 3 209}{4}

Separate the equation into 2 possible cases

x = \frac{21 + 3 209}{4} x = \frac{21 - 3 209}{4}

Solution

x_{1} = \frac{21 - 3 209}{4}, x_{2} = \frac{21 + 3 209}{4}

Alternative Form

x_{1} \approx - 5.592624, x_{2} \approx 16.092624

Solve the quadratic equation