Solve x*(2.4+5.1)/sqrt{(1-0.51)}=2^-2/0.4*(-12+8)

$$\frac{ x \times (2.4+5.1) }{ \sqrt{ (1-0.51) } } = \frac{ { 2 }^{ -2 } }{ 0.4 \times (-12+8) }$$

Solve for x

$$x=-\frac{7}{480}\approx -0.014583333$$

Steps for Solving Linear Equation

Add 2.4 and 5.1 to get 7.5.

$$\frac{x\times 7.5}{\sqrt{1-0.51}}=\frac{2^{-2}}{0.4\left(-12+8\right)}$$

Subtract 0.51 from 1 to get 0.49.

$$\frac{x\times 7.5}{\sqrt{0.49}}=\frac{2^{-2}}{0.4\left(-12+8\right)}$$

Calculate the square root of 0.49 and get 0.7.

$$\frac{x\times 7.5}{0.7}=\frac{2^{-2}}{0.4\left(-12+8\right)}$$

Divide x\times 7.5 by 0.7 to get x\times \frac{75}{7}.

$$x\times \frac{75}{7}=\frac{2^{-2}}{0.4\left(-12+8\right)}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$x\times \frac{75}{7}=\frac{\frac{1}{4}}{0.4\left(-12+8\right)}$$

Add -12 and 8 to get -4.

$$x\times \frac{75}{7}=\frac{\frac{1}{4}}{0.4\left(-4\right)}$$

Multiply 0.4 and -4 to get -1.6.

$$x\times \frac{75}{7}=\frac{\frac{1}{4}}{-1.6}$$

Express \frac{\frac{1}{4}}{-1.6} as a single fraction.

$$x\times \frac{75}{7}=\frac{1}{4\left(-1.6\right)}$$

Multiply 4 and -1.6 to get -6.4.

$$x\times \frac{75}{7}=\frac{1}{-6.4}$$

Expand \frac{1}{-6.4} by multiplying both numerator and the denominator by 10.

$$x\times \frac{75}{7}=\frac{10}{-64}$$

Reduce the fraction \frac{10}{-64} to lowest terms by extracting and canceling out 2.

$$x\times \frac{75}{7}=-\frac{5}{32}$$

Divide both sides by \frac{75}{7}.

$$x=\frac{-\frac{5}{32}}{\frac{75}{7}}$$

Express \frac{-\frac{5}{32}}{\frac{75}{7}} as a single fraction.

$$x=\frac{-5}{32\times \frac{75}{7}}$$

Multiply 32 and \frac{75}{7} to get \frac{2400}{7}.

$$x=\frac{-5}{\frac{2400}{7}}$$