X2-5x=2x-7

Solution for X2-5x=2x-7 equation:

X2-5X=2X-7

We move all terms to the left:

X2-5X-(2X-7)=0

We add all the numbers together, and all the variables

X^2-5X-(2X-7)=0

We get rid of parentheses

X^2-5X-2X+7=0

We add all the numbers together, and all the variables

X^2-7X+7=0

a = 1; b = -7; c = +7;
Δ = b2-4ac
Δ = -72-4·1·7
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{21}}{2*1}=\frac{7-\sqrt{21}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{21}}{2*1}=\frac{7+\sqrt{21}}{2}
$