3x^2-7x=11

Solution for 3x^2-7x=11 equation:

3x^2-7x=11

We move all terms to the left:

3x^2-7x-(11)=0

a = 3; b = -7; c = -11;
Δ = b2-4ac
Δ = -72-4·3·(-11)
Δ = 181
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{181}}{2*3}=\frac{7-\sqrt{181}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{181}}{2*3}=\frac{7+\sqrt{181}}{6}
$