Solve for x
x = \frac{5 \sqrt{5} + 9}{4} \approx 5.045084972
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4\sqrt{2x+3}-2\sqrt{5}-\left(-2\sqrt{5}\right)=10-\left(-2\sqrt{5}\right)
Subtract -2\sqrt{5} from both sides of the equation.
4\sqrt{2x+3}=10-\left(-2\sqrt{5}\right)
Subtracting -2\sqrt{5} from itself leaves 0.
4\sqrt{2x+3}=2\sqrt{5}+10
Subtract -2\sqrt{5} from 10.
\frac{4\sqrt{2x+3}}{4}=\frac{2\sqrt{5}+10}{4}
Divide both sides by 4.
\sqrt{2x+3}=\frac{2\sqrt{5}+10}{4}
Dividing by 4 undoes the multiplication by 4.
\sqrt{2x+3}=\frac{\sqrt{5}+5}{2}
Divide 10+2\sqrt{5} by 4.
2x+3=\frac{5\sqrt{5}+15}{2}
Square both sides of the equation.
2x+3-3=\frac{5\sqrt{5}+15}{2}-3
Subtract 3 from both sides of the equation.
2x=\frac{5\sqrt{5}+15}{2}-3
Subtracting 3 from itself leaves 0.
2x=\frac{5\sqrt{5}+9}{2}
Subtract 3 from \frac{15+5\sqrt{5}}{2}.
\frac{2x}{2}=\frac{5\sqrt{5}+9}{2\times 2}
Divide both sides by 2.
x=\frac{5\sqrt{5}+9}{2\times 2}
Dividing by 2 undoes the multiplication by 2.
x=\frac{5\sqrt{5}+9}{4}
Divide \frac{9+5\sqrt{5}}{2} by 2.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}