1+3x(+9x)=61

Solution for 1+3x(+9x)=61 equation:

1+3x(+9x)=61

We move all terms to the left:

1+3x(+9x)-(61)=0

We add all the numbers together, and all the variables

3x(+9x)-60=0

We multiply parentheses

27x^2-60=0

a = 27; b = 0; c = -60;
Δ = b2-4ac
Δ = 02-4·27·(-60)
Δ = 6480
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:

$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{5}}{2*27}=\frac{0-36\sqrt{5}}{54}
=-\frac{36\sqrt{5}}{54}
=-\frac{2\sqrt{5}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{5}}{2*27}=\frac{0+36\sqrt{5}}{54}
=\frac{36\sqrt{5}}{54}
=\frac{2\sqrt{5}}{3}
$