23x+5=10x^2

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

23x+5=10x^2

We move all terms to the left:

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

determiningTheFunctionDomain
-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{-50}{-20}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+27}{2*-10}=\frac{4}{-20}
=-1/5
$