7x^2-74x+160=0

Solution for 7x^2-74x+160=0 equation:

7x^2-74x+160=0

a = 7; b = -74; c = +160;
Δ = b2-4ac
Δ = -742-4·7·160
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-2\sqrt{249}}{2*7}=\frac{74-2\sqrt{249}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+2\sqrt{249}}{2*7}=\frac{74+2\sqrt{249}}{14}
$