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(5-u)(4u-9)=0u=
We move all terms to the left:
(5-u)(4u-9)-(0u)=0
We add all the numbers together, and all the variables
(-1u+5)(4u-9)-0u=0
We add all the numbers together, and all the variables
-1u+(-1u+5)(4u-9)=0
We multiply parentheses ..
(-4u^2+9u+20u-45)-1u=0
We get rid of parentheses
-4u^2+9u+20u-1u-45=0
We add all the numbers together, and all the variables
-4u^2+28u-45=0
a = -4; b = 28; c = -45;
Δ = b2-4ac
Δ = 282-4·(-4)·(-45)
Δ = 64
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}$$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{64}=8$$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-8}{2*-4}=\frac{-36}{-8} =4+1/2 $$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+8}{2*-4}=\frac{-20}{-8} =2+1/2 $
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