3x^2-11x=48

Solution for 3x^2-11x=48 equation:

3x^2-11x=48

We move all terms to the left:

3x^2-11x-(48)=0

a = 3; b = -11; c = -48;
Δ = b2-4ac
Δ = -112-4·3·(-48)
Δ = 697
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{-(-11)-\sqrt{697}}{2*3}=\frac{11-\sqrt{697}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{697}}{2*3}=\frac{11+\sqrt{697}}{6}
$