Solve 5/6+0,75-0,25r^2/3=r/2-(5+r)^2/12

$$\frac { 5 } { 6 } + \frac { 0,75 - 0,25 r ^ { 2 } } { 3 } = \frac { r } { 2 } - \frac { ( 5 + r ) ^ { 2 } } { 12 }$$

Solve for r

$$r=-9,5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 6;3;2;12.

$$10+4\left(0,75-0,25r^{2}\right)=6r-\left(5+r\right)^{2}$$

Use the distributive property to multiply 4 by 0,75-0,25r^{2}.

$$10+3-r^{2}=6r-\left(5+r\right)^{2}$$

Add 10 and 3 to get 13.

$$13-r^{2}=6r-\left(5+r\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5+r\right)^{2}.

$$13-r^{2}=6r-\left(25+10r+r^{2}\right)$$

To find the opposite of 25+10r+r^{2}, find the opposite of each term.

$$13-r^{2}=6r-25-10r-r^{2}$$

Combine 6r and -10r to get -4r.

$$13-r^{2}=-4r-25-r^{2}$$

Add 4r to both sides.

$$13-r^{2}+4r=-25-r^{2}$$

Add r^{2} to both sides.

$$13-r^{2}+4r+r^{2}=-25$$

Combine -r^{2} and r^{2} to get 0.

$$13+4r=-25$$

Subtract 13 from both sides.

$$4r=-25-13$$

Subtract 13 from -25 to get -38.

$$4r=-38$$

Divide both sides by 4.

$$r=\frac{-38}{4}$$

Reduce the fraction \frac{-38}{4} to lowest terms by extracting and canceling out 2.

$$r=-\frac{19}{2}$$