23-7x(x-3)+5x=10

Solution for 23-7x(x-3)+5x=10 equation:

23-7x(x-3)+5x=10

We move all terms to the left:

23-7x(x-3)+5x-(10)=0

We add all the numbers together, and all the variables

5x-7x(x-3)+13=0

We multiply parentheses

-7x^2+5x+21x+13=0

We add all the numbers together, and all the variables

-7x^2+26x+13=0

a = -7; b = 26; c = +13;
Δ = b2-4ac
Δ = 262-4·(-7)·13
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{-(26)-4\sqrt{65}}{2*-7}=\frac{-26-4\sqrt{65}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+4\sqrt{65}}{2*-7}=\frac{-26+4\sqrt{65}}{-14}
$