10.5x=x*x+5

Solution for 10.5x=x*x+5 equation:

10.5x=x*x+5

We move all terms to the left:

10.5x-(x*x+5)=0

We get rid of parentheses

10.5x-x*x-5=0

Wy multiply elements

-1x^2+10.5x-5=0

a = -1; b = 10.5; c = -5;
Δ = b2-4ac
Δ = 10.52-4·(-1)·(-5)
Δ = 90.25
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{-(10.5)-\sqrt{90.25}}{2*-1}=\frac{-10.5-\sqrt{90.25}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10.5)+\sqrt{90.25}}{2*-1}=\frac{-10.5+\sqrt{90.25}}{-2}
$