Solve -5x^2+3x-6/2-4x-8/5=5left(2-xright)left(2+xright)

$$-5 { x }^{ 2 } + \frac{ 3x-6 }{ 2 } - \frac{ 4x-8 }{ 5 } = 5 \left( 2-x \right) \left( 2+x \right)$$

Solve for x

$$x = \frac{214}{7} = 30\frac{4}{7} \approx 30.571428571$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 2,5.

$$-50x^{2}+5\left(3x-6\right)-2\left(4x-8\right)=50\left(2-x\right)\left(2+x\right)$$

Use the distributive property to multiply 5 by 3x-6.

$$-50x^{2}+15x-30-2\left(4x-8\right)=50\left(2-x\right)\left(2+x\right)$$

Use the distributive property to multiply -2 by 4x-8.

$$-50x^{2}+15x-30-8x+16=50\left(2-x\right)\left(2+x\right)$$

Combine 15x and -8x to get 7x.

$$-50x^{2}+7x-30+16=50\left(2-x\right)\left(2+x\right)$$

Add -30 and 16 to get -14.

$$-50x^{2}+7x-14=50\left(2-x\right)\left(2+x\right)$$

Use the distributive property to multiply 50 by 2-x.

$$-50x^{2}+7x-14=\left(100-50x\right)\left(2+x\right)$$

Use the distributive property to multiply 100-50x by 2+x and combine like terms.

$$-50x^{2}+7x-14=200-50x^{2}$$

Add 50x^{2} to both sides.

$$-50x^{2}+7x-14+50x^{2}=200$$

Combine -50x^{2} and 50x^{2} to get 0.

$$7x-14=200$$

Add 14 to both sides.

$$7x=200+14$$

Add 200 and 14 to get 214.

$$7x=214$$

Divide both sides by 7.

$$x=\frac{214}{7}$$