Solve sqrt{98}:(x+4)(2x-3)=6

$$\sqrt { 98 } : ( x + 4 ) ( 2 x - 3 ) = 6$$

Solve for x

$$x=\frac{231\sqrt{2}}{178}+\frac{183}{89}\approx 3.891479398$$

Steps for Solving Linear Equation

Variable x cannot be equal to -4 since division by zero is not defined. Multiply both sides of the equation by x+4.

$$\sqrt{98}\left(2x-3\right)=6\left(x+4\right)$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$7\sqrt{2}\left(2x-3\right)=6\left(x+4\right)$$

Use the distributive property to multiply 7\sqrt{2} by 2x-3.

$$14x\sqrt{2}-21\sqrt{2}=6\left(x+4\right)$$

Use the distributive property to multiply 6 by x+4.

$$14x\sqrt{2}-21\sqrt{2}=6x+24$$

Subtract 6x from both sides.

$$14x\sqrt{2}-21\sqrt{2}-6x=24$$

Add 21\sqrt{2} to both sides.

$$14x\sqrt{2}-6x=24+21\sqrt{2}$$

Combine all terms containing x.

$$\left(14\sqrt{2}-6\right)x=24+21\sqrt{2}$$

The equation is in standard form.

$$\left(14\sqrt{2}-6\right)x=21\sqrt{2}+24$$

Divide both sides by 14\sqrt{2}-6.

$$\frac{\left(14\sqrt{2}-6\right)x}{14\sqrt{2}-6}=\frac{21\sqrt{2}+24}{14\sqrt{2}-6}$$

Dividing by 14\sqrt{2}-6 undoes the multiplication by 14\sqrt{2}-6.

$$x=\frac{21\sqrt{2}+24}{14\sqrt{2}-6}$$

Divide 24+21\sqrt{2} by 14\sqrt{2}-6.

$$x=\frac{231\sqrt{2}}{178}+\frac{183}{89}$$