Solve frac{4pmsqrt{-4^2-4*(-3)*39}}{2*(-3)}=frac{4pmsqrt{-16+468}}{-6}

$$\frac { 4 \pm \sqrt { - 4 ^ { 2 } - 4 \cdot ( - 3 ) \cdot 39 } } { 2 \cdot ( - 3 ) } = \frac { 4 \pm \sqrt { - 16 + 468 } } { - 6 }$$

Verify

Solution Steps

Multiply both sides of the equation by -6.

$$4±\sqrt{-4^{2}-4\left(-3\right)\times 39}=4±\sqrt{-16+468}$$

Calculate 4 to the power of 2 and get 16.

$$4±\sqrt{-16-4\left(-3\right)\times 39}=4±\sqrt{-16+468}$$

Multiply 4 and -3 to get -12.

$$4±\sqrt{-16-\left(-12\times 39\right)}=4±\sqrt{-16+468}$$

Multiply -12 and 39 to get -468.

$$4±\sqrt{-16-\left(-468\right)}=4±\sqrt{-16+468}$$

The opposite of -468 is 468.

$$4±\sqrt{-16+468}=4±\sqrt{-16+468}$$

Add -16 and 468 to get 452.

$$4±\sqrt{452}=4±\sqrt{-16+468}$$

Factor 452=2^{2}\times 113. Rewrite the square root of the product \sqrt{2^{2}\times 113} as the product of square roots \sqrt{2^{2}}\sqrt{113}. Take the square root of 2^{2}.

$$4±2\sqrt{113}=4±\sqrt{-16+468}$$

Add -16 and 468 to get 452.

$$4±2\sqrt{113}=4±\sqrt{452}$$

Factor 452=2^{2}\times 113. Rewrite the square root of the product \sqrt{2^{2}\times 113} as the product of square roots \sqrt{2^{2}}\sqrt{113}. Take the square root of 2^{2}.

$$4±2\sqrt{113}=4±2\sqrt{113}$$

Subtract 4±2\sqrt{113} from both sides.

$$4±2\sqrt{113}-\left(4±2\sqrt{113}\right)=0$$

Combine 4±2\sqrt{113} and -\left(4±2\sqrt{113}\right) to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$