4(x-9)x+3=13

Solution for 4(x-9)x+3=13 equation:

4(x-9)x+3=13

We move all terms to the left:

4(x-9)x+3-(13)=0

We add all the numbers together, and all the variables

4(x-9)x-10=0

We multiply parentheses

4x^2-36x-10=0

a = 4; b = -36; c = -10;
Δ = b2-4ac
Δ = -362-4·4·(-10)
Δ = 1456
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:

$\sqrt{\Delta}=\sqrt{1456}=\sqrt{16*91}=\sqrt{16}*\sqrt{91}=4\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{91}}{2*4}=\frac{36-4\sqrt{91}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{91}}{2*4}=\frac{36+4\sqrt{91}}{8}
$