Solve -2x^2-6x+x+3+5x+4=0

$$- 2 x ^ { 2 } - 6 x + x + 3 + 5 x + 4 = 0$$

Solve for x

$$x = \frac{\sqrt{14}}{2} \approx 1.870828693$$

$$x = -\frac{\sqrt{14}}{2} \approx -1.870828693$$

Steps by Finding Square Root

Combine -6x and x to get -5x.

$$-2x^{2}-5x+3+5x+4=0$$

Combine -5x and 5x to get 0.

$$-2x^{2}+3+4=0$$

Add 3 and 4 to get 7.

$$-2x^{2}+7=0$$

Subtract 7 from both sides. Anything subtracted from zero gives its negation.

$$-2x^{2}=-7$$

Divide both sides by -2.

$$x^{2}=\frac{-7}{-2}$$

Fraction \frac{-7}{-2} can be simplified to \frac{7}{2} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{7}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{14}}{2} x=-\frac{\sqrt{14}}{2}$$

Steps Using the Quadratic Formula

Combine -6x and x to get -5x.

$$-2x^{2}-5x+3+5x+4=0$$

Combine -5x and 5x to get 0.

$$-2x^{2}+3+4=0$$

Add 3 and 4 to get 7.

$$-2x^{2}+7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and 7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 7}}{2\left(-2\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)\times 7}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\times 7}}{2\left(-2\right)}$$

Multiply 8 times 7.

$$x=\frac{0±\sqrt{56}}{2\left(-2\right)}$$

Take the square root of 56.

$$x=\frac{0±2\sqrt{14}}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{0±2\sqrt{14}}{-4}$$

Now solve the equation x=\frac{0±2\sqrt{14}}{-4} when ± is plus.

$$x=-\frac{\sqrt{14}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{14}}{-4} when ± is minus.

$$x=\frac{\sqrt{14}}{2}$$

The equation is now solved.

$$x=-\frac{\sqrt{14}}{2} x=\frac{\sqrt{14}}{2}$$