2w^2-11w+3-w^2+10w-25=0

Solution for 2w^2-11w+3-w^2+10w-25=0 equation:

2w^2-11w+3-w^2+10w-25=0

We add all the numbers together, and all the variables

w^2-1w-22=0

a = 1; b = -1; c = -22;
Δ = b2-4ac
Δ = -12-4·1·(-22)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{89}}{2*1}=\frac{1-\sqrt{89}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{89}}{2*1}=\frac{1+\sqrt{89}}{2}
$