2x^2+25x+50-(x^2+2x+1)=0

Solution for 2x^2+25x+50-(x^2+2x+1)=0 equation:

2x^2+25x+50-(x^2+2x+1)=0

We get rid of parentheses

2x^2-x^2+25x-2x-1+50=0

We add all the numbers together, and all the variables

x^2+23x+49=0

a = 1; b = 23; c = +49;
Δ = b2-4ac
Δ = 232-4·1·49
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-3\sqrt{37}}{2*1}=\frac{-23-3\sqrt{37}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+3\sqrt{37}}{2*1}=\frac{-23+3\sqrt{37}}{2}
$