X^2+3=20x-5

Solution for X^2+3=20x-5 equation:

X^2+3=20X-5

We move all terms to the left:

X^2+3-(20X-5)=0

We get rid of parentheses

X^2-20X+5+3=0

We add all the numbers together, and all the variables

X^2-20X+8=0

a = 1; b = -20; c = +8;
Δ = b2-4ac
Δ = -202-4·1·8
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{23}}{2*1}=\frac{20-4\sqrt{23}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{23}}{2*1}=\frac{20+4\sqrt{23}}{2}
$