Solve 2.7738=4E-5x^2-27*1x+5139*5

$$2.7738 = 4E-5 { x }^{ 2 } -27 \cdot 1x+5139 \cdot 5$$

Solve for E

$$E=\frac{5x^{2}}{4}+\frac{27x}{4}-6423.05655$$

Steps for Solving Linear Equation

Multiply 27 and 1 to get 27.

$$2.7738=4E-5x^{2}-27x+5139\times 5$$

Multiply 5139 and 5 to get 25695.

$$2.7738=4E-5x^{2}-27x+25695$$

Swap sides so that all variable terms are on the left hand side.

$$4E-5x^{2}-27x+25695=2.7738$$

Add 5x^{2} to both sides.

$$4E-27x+25695=2.7738+5x^{2}$$

Add 27x to both sides.

$$4E+25695=2.7738+5x^{2}+27x$$

Subtract 25695 from both sides.

$$4E=2.7738+5x^{2}+27x-25695$$

Subtract 25695 from 2.7738 to get -25692.2262.

$$4E=-25692.2262+5x^{2}+27x$$

The equation is in standard form.

$$4E=5x^{2}+27x-25692.2262$$

Divide both sides by 4.

$$\frac{4E}{4}=\frac{5x^{2}+27x-25692.2262}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$E=\frac{5x^{2}+27x-25692.2262}{4}$$

Divide -25692.2262+5x^{2}+27x by 4.

$$E=\frac{5x^{2}}{4}+\frac{27x}{4}-\frac{128461131}{20000}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{200000E+1286433810}}{500}-2.7$$

$$x=\frac{\sqrt{200000E+1286433810}}{500}-2.7$$

Solve for x

$$x=-\frac{\sqrt{200000E+1286433810}}{500}-2.7$$

$$x=\frac{\sqrt{200000E+1286433810}}{500}-2.7\text{, }E\geq -\frac{128643381}{20000}$$