Solve 13x+6(2x-5)=sqrt{2}x+6

$$13x+6(2x-5)= \sqrt{ 2 } x+6$$

Solve for x

$$x = \frac{36 {(\sqrt{2} + 25)}}{623} \approx 1.526342999$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6 by 2x-5.

$$13x+12x-30=\sqrt{2}x+6$$

Combine 13x and 12x to get 25x.

$$25x-30=\sqrt{2}x+6$$

Subtract \sqrt{2}x from both sides.

$$25x-30-\sqrt{2}x=6$$

Add 30 to both sides.

$$25x-\sqrt{2}x=6+30$$

Add 6 and 30 to get 36.

$$25x-\sqrt{2}x=36$$

Combine all terms containing x.

$$\left(25-\sqrt{2}\right)x=36$$

Divide both sides by 25-\sqrt{2}.

$$\frac{\left(25-\sqrt{2}\right)x}{25-\sqrt{2}}=\frac{36}{25-\sqrt{2}}$$

Dividing by 25-\sqrt{2} undoes the multiplication by 25-\sqrt{2}.

$$x=\frac{36}{25-\sqrt{2}}$$

Divide 36 by 25-\sqrt{2}.

$$x=\frac{36\sqrt{2}+900}{623}$$