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(u)(4u-24)=36
We move all terms to the left:
(u)(4u-24)-(36)=0
We multiply parentheses
4u^2-24u-36=0
a = 4; b = -24; c = -36;
Δ = b2-4ac
Δ = -242-4·4·(-36)
Δ = 1152
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:u_{1}=\frac{-b-\sqrt{\Delta}}{2a}u_{2}=\frac{-b+\sqrt{\Delta}}{2a}
The end solution:
\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{2}}{2*4}=\frac{24-24\sqrt{2}}{8}u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{2}}{2*4}=\frac{24+24\sqrt{2}}{8}
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