10x^2-20x-23=-7

Solution for 10x^2-20x-23=-7 equation:

10x^2-20x-23=-7

We move all terms to the left:

10x^2-20x-23-(-7)=0

We add all the numbers together, and all the variables

10x^2-20x-16=0

a = 10; b = -20; c = -16;
Δ = b2-4ac
Δ = -202-4·10·(-16)
Δ = 1040
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:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{65}}{2*10}=\frac{20-4\sqrt{65}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{65}}{2*10}=\frac{20+4\sqrt{65}}{20}
$