3x^2-7x=165

Solution for 3x^2-7x=165 equation:

3x^2-7x=165

We move all terms to the left:

3x^2-7x-(165)=0

a = 3; b = -7; c = -165;
Δ = b2-4ac
Δ = -72-4·3·(-165)
Δ = 2029
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{-(-7)-\sqrt{2029}}{2*3}=\frac{7-\sqrt{2029}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{2029}}{2*3}=\frac{7+\sqrt{2029}}{6}
$