3x2+5x=19

Solution for 3x2+5x=19 equation:

3x^2+5x=19

We move all terms to the left:

3x^2+5x-(19)=0

a = 3; b = 5; c = -19;
Δ = b2-4ac
Δ = 52-4·3·(-19)
Δ = 253
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{-(5)-\sqrt{253}}{2*3}=\frac{-5-\sqrt{253}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{253}}{2*3}=\frac{-5+\sqrt{253}}{6}
$