10x2-23x=5

Solution for 10x2-23x=5 equation:

10x^2-23x=5

We move all terms to the left:

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

a = 10; b = -23; c = -5;
Δ = b2-4ac
Δ = -232-4·10·(-5)
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*10}=\frac{-4}{20}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+27}{2*10}=\frac{50}{20}
=2+1/2
$