Solve 4(5x^2)=10(2x-3) 15

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{15 - 3 15}{2}, x_{2} = \frac{15 + 3 15}{2}

Alternative Form

x_{1} \approx 1.690525, x_{2} \approx 13.309475

Evaluate

4 \times 5 x^{2} = 10 (2 x - 3) \times 15

Multiply the numbers

20 x^{2} = 10 (2 x - 3) \times 15

Multiply the terms

20 x^{2} = 150 (2 x - 3)

Expand the expression

More Steps

20 x^{2} = 300 x - 450

Move the expression to the left side

20 x^{2} - 300 x + 450 = 0

Substitute a= 20,b= - 300 and c= 450 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{300 \pm ( - 300 ) ^{2} - 4 \times 20 \times 450}{2 \times 20}

Simplify the expression

x = \frac{300 \pm ( - 300 ) ^{2} - 4 \times 20 \times 450}{40}

Simplify the expression

More Steps

x = \frac{300 \pm 30 0 ^{2} - 36000}{40}

Simplify the radical expression

More Steps

x = \frac{300 \pm 60 15}{40}

Separate the equation into 2 possible cases

x = \frac{300 + 60 15}{40} x = \frac{300 - 60 15}{40}

Simplify the expression

More Steps

x = \frac{15 + 3 15}{2} x = \frac{300 - 60 15}{40}

Simplify the expression

More Steps

x = \frac{15 + 3 15}{2} x = \frac{15 - 3 15}{2}

Solution

x_{1} = \frac{15 - 3 15}{2}, x_{2} = \frac{15 + 3 15}{2}

Alternative Form

x_{1} \approx 1.690525, x_{2} \approx 13.309475

Show Solution