If the tangent to the curve $y=x^{3}-x^{2}+x$ at the point $(a, b)$ is also tangent to the curve $y = 5{x^2} + 2x - 25$ at the point (2, $-$1), then $|2a + 9b|$ is equal to __________.

Slope of tangent to curve $y=5 x^{2}+2 x-25$ <br/><br/>$=m=\left(\frac{d y}{d x}\right)_{\mathrm{at}(2,-1)}=22$ <br/><br/>$\therefore \quad$ Equation of tangent $: y+1=22(x-2)$ <br/><br/>$\therefore \quad y=22 x-45$. <br/><br/>Slope of tangent to $y=x^{3}-x^{2}+x$ at point $(a, b)$ <br/><br/>$=3 a^{2}-2 a+1$ <br/><br/>$3 a^{2}-2 a+1=22$ <br/><br/>$3 a^{2}-2 a-21=0$ <br/><br/>$\therefore \quad a=3$ or $-\frac{7}{3}$ <br/><br/>Also $b=a^{3}-a^{2}+a$ <br/><br/>Then $(a, b)=(3,21)$ or $\left(-\frac{7}{3},-\frac{151}{9}\right)$. <br/><br/>$\left(-\frac{7}{3},-\frac{151}{9}\right)$ does not satisfy the equation of tangent <br/><br/>$\therefore \quad a=3, b=21$ <br/><br/>$\therefore|2 a+9 b|=195$