10x^2-22x-15=0

Solution for 10x^2-22x-15=0 equation:

10x^2-22x-15=0

a = 10; b = -22; c = -15;
Δ = b2-4ac
Δ = -222-4·10·(-15)
Δ = 1084
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:

$\sqrt{\Delta}=\sqrt{1084}=\sqrt{4*271}=\sqrt{4}*\sqrt{271}=2\sqrt{271}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{271}}{2*10}=\frac{22-2\sqrt{271}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{271}}{2*10}=\frac{22+2\sqrt{271}}{20}
$