3x^2+4x=100

Solution for 3x^2+4x=100 equation:

3x^2+4x=100

We move all terms to the left:

3x^2+4x-(100)=0

a = 3; b = 4; c = -100;
Δ = b2-4ac
Δ = 42-4·3·(-100)
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{19}}{2*3}=\frac{-4-8\sqrt{19}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{19}}{2*3}=\frac{-4+8\sqrt{19}}{6}
$