3x2+4x=11

Solution for 3x2+4x=11 equation:

3x^2+4x=11

We move all terms to the left:

3x^2+4x-(11)=0

a = 3; b = 4; c = -11;
Δ = b2-4ac
Δ = 42-4·3·(-11)
Δ = 148
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{37}}{2*3}=\frac{-4-2\sqrt{37}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{37}}{2*3}=\frac{-4+2\sqrt{37}}{6}
$