5x^2-30x-400=0

Solution for 5x^2-30x-400=0 equation:

5x^2-30x-400=0

a = 5; b = -30; c = -400;
Δ = b2-4ac
Δ = -302-4·5·(-400)
Δ = 8900
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:

$\sqrt{\Delta}=\sqrt{8900}=\sqrt{100*89}=\sqrt{100}*\sqrt{89}=10\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{89}}{2*5}=\frac{30-10\sqrt{89}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{89}}{2*5}=\frac{30+10\sqrt{89}}{10}
$