x(3x-29)=75

Solution for x(3x-29)=75 equation:

x(3x-29)=75

We move all terms to the left:

x(3x-29)-(75)=0

We multiply parentheses

3x^2-29x-75=0

a = 3; b = -29; c = -75;
Δ = b2-4ac
Δ = -292-4·3·(-75)
Δ = 1741
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-\sqrt{1741}}{2*3}=\frac{29-\sqrt{1741}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{1741}}{2*3}=\frac{29+\sqrt{1741}}{6}
$