Solve -9/2=a*(-5/8+7/2)^2+10/3

$$- \frac { 9 } { 2 } = a \cdot ( - \frac { 5 } { 8 } + \frac { 7 } { 2 } ) ^ { 2 } + \frac { 10 } { 3 }$$

Solve for a

$$a=-\frac{1504}{1587}\approx -0.947700063$$

Steps for Solving Linear Equation

Add -\frac{5}{8} and \frac{7}{2} to get \frac{23}{8}.

$$-\frac{9}{2}=a\times \left(\frac{23}{8}\right)^{2}+\frac{10}{3}$$

Calculate \frac{23}{8} to the power of 2 and get \frac{529}{64}.

$$-\frac{9}{2}=a\times \frac{529}{64}+\frac{10}{3}$$

Swap sides so that all variable terms are on the left hand side.

$$a\times \frac{529}{64}+\frac{10}{3}=-\frac{9}{2}$$

Subtract \frac{10}{3} from both sides.

$$a\times \frac{529}{64}=-\frac{9}{2}-\frac{10}{3}$$

Subtract \frac{10}{3} from -\frac{9}{2} to get -\frac{47}{6}.

$$a\times \frac{529}{64}=-\frac{47}{6}$$

Multiply both sides by \frac{64}{529}, the reciprocal of \frac{529}{64}.

$$a=-\frac{47}{6}\times \frac{64}{529}$$

Multiply -\frac{47}{6} and \frac{64}{529} to get -\frac{1504}{1587}.

$$a=-\frac{1504}{1587}$$