5x^2-10=-23x

Solution for 5x^2-10=-23x equation:

5x^2-10=-23x

We move all terms to the left:

5x^2-10-(-23x)=0

We get rid of parentheses

5x^2+23x-10=0

a = 5; b = 23; c = -10;
Δ = b2-4ac
Δ = 232-4·5·(-10)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-27}{2*5}=\frac{-50}{10}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+27}{2*5}=\frac{4}{10}
=2/5
$