7x^2-109x+252=0

Solution for 7x^2-109x+252=0 equation:

7x^2-109x+252=0

a = 7; b = -109; c = +252;
Δ = b2-4ac
Δ = -1092-4·7·252
Δ = 4825
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:

$\sqrt{\Delta}=\sqrt{4825}=\sqrt{25*193}=\sqrt{25}*\sqrt{193}=5\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-109)-5\sqrt{193}}{2*7}=\frac{109-5\sqrt{193}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-109)+5\sqrt{193}}{2*7}=\frac{109+5\sqrt{193}}{14}
$