Question 880251
Re TY
Sry, You did not say You were wanting the formulas for solving cubic equations:
See x[2]below: Plug and Play, the value of a would simply be:
a = {{{1 +(-.5)root(3, 540+540)/6root(3,2)}}} Answer formatted as directed.  
Recommend using a Graphing calculator to find the real root
 Or cubic equation Calculator to find all:
f(x)=2x^3- 6x^2+6x-7 |format ax^2 + bx^2 + cx + d
3 Roots, 2 imaginary  (nearest 4 decimal places)
x is 2.3572, .3214 + 1.1754i, .3214 - 1.1754i
a = 0.3213955958512734 
X[1] = {{{-b/(3*a) +
         root(3,(-2*b^3+9*a*b*c-27*a^2*d+
         sqrt(4*(-b^2+3*a*c)^3+(-2*b^3+9*a*b*c-27*a^2*d)^2)))/
         (3*root(3,2)*a)}}}
x[2] = {{{-b/(3*a) +((-1+i*sqrt(3))/2)(root(3,(-2*b^3+9*a*b*c-27*a^2*d+
         sqrt(4*(-b^2+3*a*c)^3+(-2*b^3+9*a*b*c-27*a^2*d)^2))))/
         (3*root(3,2)a)+ ((-1-i*sqrt(3))/2)(root(3,(-2*b^3+9*a*b*c-27*a^2*d-
         sqrt(4*(-b^2+3*a*c)^3+(-2*b^3+9*a*b*c-27*a^2*d)^2))))/ (3*root(3,2)a) }}}

X[3] = {{{-b/(3*a) +(-1-i*sqrt(3))/2*root(3,(-2*b^3+9*a*b*c-27*a^2*d+
         sqrt(4*(-b^2+3*a*c)^3+(-2*b^3+9*a*b*c-27*a^2*d)^2)))/
         (3*root(3,2)a)+ (-1+i*sqrt(3))/2*root(3,(-2*b^3+9*a*b*c-27*a^2*d-
         sqrt(4*(-b^2+3*a*c)^3+(-2*b^3+9*a*b*c-27*a^2*d)^2)))/
         (3*root(3,2)a) }}}