7x^2-46x-45=0

Solution for 7x^2-46x-45=0 equation:

7x^2-46x-45=0

a = 7; b = -46; c = -45;
Δ = b2-4ac
Δ = -462-4·7·(-45)
Δ = 3376
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:

$\sqrt{\Delta}=\sqrt{3376}=\sqrt{16*211}=\sqrt{16}*\sqrt{211}=4\sqrt{211}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-4\sqrt{211}}{2*7}=\frac{46-4\sqrt{211}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+4\sqrt{211}}{2*7}=\frac{46+4\sqrt{211}}{14}
$