Solve 8x - 3 = x^2

Evaluate

8 x - 3 = x^{2}

Swap the sides

x^{2} = 8 x - 3

Move the expression to the left side

x^{2} - 8 x + 3 = 0

Substitute a= 1,b= - 8 and c= 3 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 3}{2}

Simplify the expression

More Steps

x = \frac{8 \pm 52}{2}

Simplify the radical expression

More Steps

x = \frac{8 \pm 2 13}{2}

Separate the equation into 2 possible cases

x = \frac{8 + 2 13}{2} x = \frac{8 - 2 13}{2}

Simplify the expression

More Steps

x = 4 + 13 x = \frac{8 - 2 13}{2}

Simplify the expression

More Steps

x = 4 + 13 x = 4 - 13

Solution

x_{1} = 4 - 13, x_{2} = 4 + 13

Alternative Form

x_{1} \approx 0.394449, x_{2} \approx 7.605551

Solve the quadratic equation