3x(7x+61)=29

Solution for 3x(7x+61)=29 equation:

3x(7x+61)=29

We move all terms to the left:

3x(7x+61)-(29)=0

We multiply parentheses

21x^2+183x-29=0

a = 21; b = 183; c = -29;
Δ = b2-4ac
Δ = 1832-4·21·(-29)
Δ = 35925
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:

$\sqrt{\Delta}=\sqrt{35925}=\sqrt{25*1437}=\sqrt{25}*\sqrt{1437}=5\sqrt{1437}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(183)-5\sqrt{1437}}{2*21}=\frac{-183-5\sqrt{1437}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(183)+5\sqrt{1437}}{2*21}=\frac{-183+5\sqrt{1437}}{42}
$