X2-3x=5-3x

Solution for X2-3x=5-3x equation:

X2-3X=5-3X

We move all terms to the left:

X2-3X-(5-3X)=0

We add all the numbers together, and all the variables

X2-3X-(-3X+5)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

X^2-5=0

a = 1; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·1·(-5)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5}}{2*1}=\frac{0-2\sqrt{5}}{2}
=-\frac{2\sqrt{5}}{2}
=-\sqrt{5}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5}}{2*1}=\frac{0+2\sqrt{5}}{2}
=\frac{2\sqrt{5}}{2}
=\sqrt{5}
$