Calculate $\sqrt{-2x-1}$ to the power of $2$ and get $-2x-1$.
$$4\left(-2x-1\right)=\left(-7+2x\right)^{2}$$
Use the distributive property to multiply $4$ by $-2x-1$.
$$-8x-4=\left(-7+2x\right)^{2}$$
Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(-7+2x\right)^{2}$.
$$-8x-4=49-28x+4x^{2}$$
Subtract $49$ from both sides.
$$-8x-4-49=-28x+4x^{2}$$
Subtract $49$ from $-4$ to get $-53$.
$$-8x-53=-28x+4x^{2}$$
Add $28x$ to both sides.
$$-8x-53+28x=4x^{2}$$
Combine $-8x$ and $28x$ to get $20x$.
$$20x-53=4x^{2}$$
Subtract $4x^{2}$ from both sides.
$$20x-53-4x^{2}=0$$
All equations of the form $ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$. The quadratic formula gives two solutions, one when $±$ is addition and one when it is subtraction.
$$-4x^{2}+20x-53=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $-4$ for $a$, $20$ for $b$, and $-53$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
