5x^2+10x-143=0

Solution for 5x^2+10x-143=0 equation:

5x^2+10x-143=0

a = 5; b = 10; c = -143;
Δ = b2-4ac
Δ = 102-4·5·(-143)
Δ = 2960
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:

$\sqrt{\Delta}=\sqrt{2960}=\sqrt{16*185}=\sqrt{16}*\sqrt{185}=4\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{185}}{2*5}=\frac{-10-4\sqrt{185}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{185}}{2*5}=\frac{-10+4\sqrt{185}}{10}
$