2x^2-11=3x

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

2x^2-11=3x

We move all terms to the left:

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

a = 2; b = -3; c = -11;
Δ = b2-4ac
Δ = -32-4·2·(-11)
Δ = 97
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{-(-3)-\sqrt{97}}{2*2}=\frac{3-\sqrt{97}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{97}}{2*2}=\frac{3+\sqrt{97}}{4}
$