(2w+10)w=310

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Solution for (2w+10)w=310 equation:



(2w+10)w=310
We move all terms to the left:
(2w+10)w-(310)=0
We multiply parentheses
2w^2+10w-310=0
a = 2; b = 10; c = -310;
Δ = b2-4ac
Δ = 102-4·2·(-310)
Δ = 2580
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{2580}=\sqrt{4*645}=\sqrt{4}*\sqrt{645}=2\sqrt{645}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{645}}{2*2}=\frac{-10-2\sqrt{645}}{4} $
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{645}}{2*2}=\frac{-10+2\sqrt{645}}{4} $

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