5-x2=5x-7

Solution for 5-x2=5x-7 equation:

5-x2=5x-7

We move all terms to the left:

5-x2-(5x-7)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-5x+12=0

a = -1; b = -5; c = +12;
Δ = b2-4ac
Δ = -52-4·(-1)·12
Δ = 73
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{73}}{2*-1}=\frac{5-\sqrt{73}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{73}}{2*-1}=\frac{5+\sqrt{73}}{-2}
$