(3x^2)-(18x)+(7)=61

Solution for (3x^2)-(18x)+(7)=61 equation:

(3x^2)-(18x)+(7)=61

We move all terms to the left:

(3x^2)-(18x)+(7)-(61)=0

We add all the numbers together, and all the variables

3x^2-18x-54=0

a = 3; b = -18; c = -54;
Δ = b2-4ac
Δ = -182-4·3·(-54)
Δ = 972
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18\sqrt{3}}{2*3}=\frac{18-18\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18\sqrt{3}}{2*3}=\frac{18+18\sqrt{3}}{6}
$