10x^2-30x-32=0

Solution for 10x^2-30x-32=0 equation:

10x^2-30x-32=0

a = 10; b = -30; c = -32;
Δ = b2-4ac
Δ = -302-4·10·(-32)
Δ = 2180
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:

$\sqrt{\Delta}=\sqrt{2180}=\sqrt{4*545}=\sqrt{4}*\sqrt{545}=2\sqrt{545}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{545}}{2*10}=\frac{30-2\sqrt{545}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{545}}{2*10}=\frac{30+2\sqrt{545}}{20}
$