11(14x^2-41x+15)=0

Solution for 11(14x^2-41x+15)=0 equation:

11(14x^2-41x+15)=0

We multiply parentheses

154x^2-451x+165=0

a = 154; b = -451; c = +165;
Δ = b2-4ac
Δ = -4512-4·154·165
Δ = 101761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{101761}=319$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-451)-319}{2*154}=\frac{132}{308}
=3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-451)+319}{2*154}=\frac{770}{308}
=2+1/2
$