3x^2-7x+4=19

Solution for 3x^2-7x+4=19 equation:

3x^2-7x+4=19

We move all terms to the left:

3x^2-7x+4-(19)=0

We add all the numbers together, and all the variables

3x^2-7x-15=0

a = 3; b = -7; c = -15;
Δ = b2-4ac
Δ = -72-4·3·(-15)
Δ = 229
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{-(-7)-\sqrt{229}}{2*3}=\frac{7-\sqrt{229}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{229}}{2*3}=\frac{7+\sqrt{229}}{6}
$