7x^2-96x+176=0

Solution for 7x^2-96x+176=0 equation:

7x^2-96x+176=0

a = 7; b = -96; c = +176;
Δ = b2-4ac
Δ = -962-4·7·176
Δ = 4288
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:

$\sqrt{\Delta}=\sqrt{4288}=\sqrt{64*67}=\sqrt{64}*\sqrt{67}=8\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-8\sqrt{67}}{2*7}=\frac{96-8\sqrt{67}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+8\sqrt{67}}{2*7}=\frac{96+8\sqrt{67}}{14}
$