Solve Delta=(6a)^2-4x3*3(a+2)70

$$\Delta = ( 6 a ) ^ { 2 } - 4 x 3 \times 3 ( a + 2 ) 70$$

Solve for x_3

$$\left\{\begin{matrix}x_{3}=\frac{36a^{2}-\Delta }{840\left(a+2\right)}\text{, }&a\neq -2\\x_{3}\in \mathrm{R}\text{, }&\Delta =144\text{ and }a=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

Expand \left(6a\right)^{2}.

$$\Delta =6^{2}a^{2}-4x_{3}\times 3\left(a+2\right)\times 70$$

Calculate 6 to the power of 2 and get 36.

$$\Delta =36a^{2}-4x_{3}\times 3\left(a+2\right)\times 70$$

Multiply 4 and 3 to get 12.

$$\Delta =36a^{2}-12x_{3}\left(a+2\right)\times 70$$

Multiply 12 and 70 to get 840.

$$\Delta =36a^{2}-840x_{3}\left(a+2\right)$$

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

$$36a^{2}-840x_{3}\left(a+2\right)=\Delta$$

Use the distributive property to multiply -840x_{3} by a+2.

$$36a^{2}-840x_{3}a-1680x_{3}=\Delta$$

Subtract 36a^{2} from both sides.

$$-840x_{3}a-1680x_{3}=\Delta -36a^{2}$$

Combine all terms containing x_{3}.

$$\left(-840a-1680\right)x_{3}=\Delta -36a^{2}$$

Divide both sides by -840a-1680.

$$\frac{\left(-840a-1680\right)x_{3}}{-840a-1680}=\frac{\Delta -36a^{2}}{-840a-1680}$$

Dividing by -840a-1680 undoes the multiplication by -840a-1680.

$$x_{3}=\frac{\Delta -36a^{2}}{-840a-1680}$$

Divide -36a^{2}+\Delta by -840a-1680.

$$x_{3}=-\frac{\Delta -36a^{2}}{840\left(a+2\right)}$$

Solve for a

$$a=-\frac{\sqrt{4900x_{3}^{2}+1680x_{3}+\Delta }}{6}+\frac{35x_{3}}{3}$$

$$a=\frac{\sqrt{4900x_{3}^{2}+1680x_{3}+\Delta }}{6}+\frac{35x_{3}}{3}\text{, }\Delta \geq -4900x_{3}^{2}-1680x_{3}$$