x^2+10x-73=-3

Solution for x^2+10x-73=-3 equation:

x^2+10x-73=-3

We move all terms to the left:

x^2+10x-73-(-3)=0

We add all the numbers together, and all the variables

x^2+10x-70=0

a = 1; b = 10; c = -70;
Δ = b2-4ac
Δ = 102-4·1·(-70)
Δ = 380
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:

$\sqrt{\Delta}=\sqrt{380}=\sqrt{4*95}=\sqrt{4}*\sqrt{95}=2\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{95}}{2*1}=\frac{-10-2\sqrt{95}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{95}}{2*1}=\frac{-10+2\sqrt{95}}{2}
$