2.5x^2-130x-650=0

Solution for 2.5x^2-130x-650=0 equation:

2.5x^2-130x-650=0

a = 2.5; b = -130; c = -650;
Δ = b2-4ac
Δ = -1302-4·2.5·(-650)
Δ = 23400
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:

$\sqrt{\Delta}=\sqrt{23400}=\sqrt{900*26}=\sqrt{900}*\sqrt{26}=30\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-30\sqrt{26}}{2*2.5}=\frac{130-30\sqrt{26}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+30\sqrt{26}}{2*2.5}=\frac{130+30\sqrt{26}}{5}
$