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(2x)(x+4.5)=35
We move all terms to the left:
(2x)(x+4.5)-(35)=0
We multiply parentheses
2x^2+9x-35=0
a = 2; b = 9; c = -35;
Δ = b2-4ac
Δ = 92-4·2·(-35)
Δ = 361
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{361}=19$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-19}{2*2}=\frac{-28}{4} =-7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+19}{2*2}=\frac{10}{4} =2+1/2 $
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