Solve 5x ^ 2 = 4x + 7

Evaluate

5 x^{2} = 4 x + 7

Move the expression to the left side

5 x^{2} - 4 x - 7 = 0

Substitute a= 5,b= - 4 and c= - 7 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{4 \pm ( - 4 ) ^{2} - 4 \times 5 ( - 7 )}{2 \times 5}

Simplify the expression

x = \frac{4 \pm ( - 4 ) ^{2} - 4 \times 5 ( - 7 )}{10}

Simplify the expression

More Steps

x = \frac{4 \pm 156}{10}

Simplify the radical expression

More Steps

x = \frac{4 \pm 2 39}{10}

Separate the equation into 2 possible cases

x = \frac{4 + 2 39}{10} x = \frac{4 - 2 39}{10}

Simplify the expression

More Steps

x = \frac{2 + 39}{5} x = \frac{4 - 2 39}{10}

Simplify the expression

More Steps

x = \frac{2 + 39}{5} x = \frac{2 - 39}{5}

Solution

x_{1} = \frac{2 - 39}{5}, x_{2} = \frac{2 + 39}{5}

Alternative Form

x_{1} \approx - 0.849, x_{2} \approx 1.649

Solve the quadratic equation