X(X+23)-10x+3x^2=0

Solution for X(X+23)-10x+3x^2=0 equation:

X(X+23)-10X+3X^2=0

We add all the numbers together, and all the variables

3X^2-10X+X(X+23)=0

We multiply parentheses

3X^2+X^2-10X+23X=0

We add all the numbers together, and all the variables

4X^2+13X=0

a = 4; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·4·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*4}=\frac{-26}{8}
=-3+1/4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*4}=\frac{0}{8}
=0
$