Solve 10x-3(x^2)=1

Evaluate

10 x - 3 x^{2} = 1

Move the expression to the left side

10 x - 3 x^{2} - 1 = 0

Rewrite in standard form

- 3 x^{2} + 10 x - 1 = 0

Multiply both sides

3 x^{2} - 10 x + 1 = 0

Substitute a= 3,b= - 10 and c= 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{10 \pm ( - 10 ) ^{2} - 4 \times 3}{2 \times 3}

Simplify the expression

x = \frac{10 \pm ( - 10 ) ^{2} - 4 \times 3}{6}

Simplify the expression

More Steps

x = \frac{10 \pm 88}{6}

Simplify the radical expression

More Steps

x = \frac{10 \pm 2 22}{6}

Separate the equation into 2 possible cases

x = \frac{10 + 2 22}{6} x = \frac{10 - 2 22}{6}

Simplify the expression

More Steps

x = \frac{5 + 22}{3} x = \frac{10 - 2 22}{6}

Simplify the expression

More Steps

x = \frac{5 + 22}{3} x = \frac{5 - 22}{3}

Solution

x_{1} = \frac{5 - 22}{3}, x_{2} = \frac{5 + 22}{3}

Alternative Form

x_{1} \approx 0.103195, x_{2} \approx 3.230139

Solve the quadratic equation