7-5x=x2

Solution for 7-5x=x2 equation:

7-5x=x2

We move all terms to the left:

7-5x-(x2)=0

We add all the numbers together, and all the variables

-1x^2-5x+7=0

a = -1; b = -5; c = +7;
Δ = b2-4ac
Δ = -52-4·(-1)·7
Δ = 53
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{-(-5)-\sqrt{53}}{2*-1}=\frac{5-\sqrt{53}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{53}}{2*-1}=\frac{5+\sqrt{53}}{-2}
$