5x^2-40x-35=0

Solution for 5x^2-40x-35=0 equation:

5x^2-40x-35=0

a = 5; b = -40; c = -35;
Δ = b2-4ac
Δ = -402-4·5·(-35)
Δ = 2300
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:

$\sqrt{\Delta}=\sqrt{2300}=\sqrt{100*23}=\sqrt{100}*\sqrt{23}=10\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-10\sqrt{23}}{2*5}=\frac{40-10\sqrt{23}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+10\sqrt{23}}{2*5}=\frac{40+10\sqrt{23}}{10}
$