Solve y=36x^2+6*(10-x)^2/20*9

$$y = 36 x ^ { 2 } + \frac { 6 \cdot ( 10 - x ) ^ { 2 } } { 20 } \cdot 9$$

Solve for y

$$y=\frac{387x^{2}}{10}-54x+270$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(10-x\right)^{2}.

$$y=36x^{2}+\frac{6\left(100-20x+x^{2}\right)}{20}\times 9$$

Divide 6\left(100-20x+x^{2}\right) by 20 to get \frac{3}{10}\left(100-20x+x^{2}\right).

$$y=36x^{2}+\frac{3}{10}\left(100-20x+x^{2}\right)\times 9$$

Use the distributive property to multiply \frac{3}{10} by 100-20x+x^{2}.

$$y=36x^{2}+\left(30-6x+\frac{3}{10}x^{2}\right)\times 9$$

Use the distributive property to multiply 30-6x+\frac{3}{10}x^{2} by 9.

$$y=36x^{2}+270-54x+\frac{27}{10}x^{2}$$

Combine 36x^{2} and \frac{27}{10}x^{2} to get \frac{387}{10}x^{2}.

$$y=\frac{387}{10}x^{2}+270-54x$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{430y-108000}}{129}+\frac{30}{43}$$

$$x=\frac{\sqrt{430y-108000}}{129}+\frac{30}{43}$$

Solve for x

$$x=-\frac{\sqrt{430y-108000}}{129}+\frac{30}{43}$$

$$x=\frac{\sqrt{430y-108000}}{129}+\frac{30}{43}\text{, }y\geq \frac{10800}{43}$$