3x^2+18x=51

Solution for 3x^2+18x=51 equation:

3x^2+18x=51

We move all terms to the left:

3x^2+18x-(51)=0

a = 3; b = 18; c = -51;
Δ = b2-4ac
Δ = 182-4·3·(-51)
Δ = 936
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:

$\sqrt{\Delta}=\sqrt{936}=\sqrt{36*26}=\sqrt{36}*\sqrt{26}=6\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{26}}{2*3}=\frac{-18-6\sqrt{26}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{26}}{2*3}=\frac{-18+6\sqrt{26}}{6}
$