Solve (3-x/2)^2+5-y/4=0

$$( \frac { 3 - x } { 2 } ) ^ { 2 } + \frac { 5 - y } { 4 } = 0$$

Solve for y

$$y=\left(x-3\right)^{2}+5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4.

$$4\times \left(\frac{3-x}{2}\right)^{2}+5-y=0$$

To raise \frac{3-x}{2} to a power, raise both numerator and denominator to the power and then divide.

$$4\times \frac{\left(3-x\right)^{2}}{2^{2}}+5-y=0$$

Express 4\times \frac{\left(3-x\right)^{2}}{2^{2}} as a single fraction.

$$\frac{4\left(3-x\right)^{2}}{2^{2}}+5-y=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5-y times \frac{2^{2}}{2^{2}}.

$$\frac{4\left(3-x\right)^{2}}{2^{2}}+\frac{\left(5-y\right)\times 2^{2}}{2^{2}}=0$$

Since \frac{4\left(3-x\right)^{2}}{2^{2}} and \frac{\left(5-y\right)\times 2^{2}}{2^{2}} have the same denominator, add them by adding their numerators.

$$\frac{4\left(3-x\right)^{2}+\left(5-y\right)\times 2^{2}}{2^{2}}=0$$

Do the multiplications in 4\left(3-x\right)^{2}+\left(5-y\right)\times 2^{2}.

$$\frac{36-24x+4x^{2}+20-4y}{2^{2}}=0$$

Combine like terms in 36-24x+4x^{2}+20-4y.

$$\frac{56-24x+4x^{2}-4y}{2^{2}}=0$$

Calculate 2 to the power of 2 and get 4.

$$\frac{56-24x+4x^{2}-4y}{4}=0$$

Divide each term of 56-24x+4x^{2}-4y by 4 to get 14-6x+x^{2}-y.

$$14-6x+x^{2}-y=0$$

Subtract 14 from both sides. Anything subtracted from zero gives its negation.

$$-6x+x^{2}-y=-14$$

Add 6x to both sides.

$$x^{2}-y=-14+6x$$

Subtract x^{2} from both sides.

$$-y=-14+6x-x^{2}$$

The equation is in standard form.

$$-y=-x^{2}+6x-14$$

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{-x^{2}+6x-14}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{-x^{2}+6x-14}{-1}$$

Divide -14+6x-x^{2} by -1.

$$y=x^{2}-6x+14$$

Solve for x (complex solution)

$$x=\sqrt{y-5}+3$$

$$x=-\sqrt{y-5}+3$$

Solve for x

$$x=\sqrt{y-5}+3$$

$$x=-\sqrt{y-5}+3\text{, }y\geq 5$$