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4x(5x+2)=9
We move all terms to the left:
4x(5x+2)-(9)=0
We multiply parentheses
20x^2+8x-9=0
a = 20; b = 8; c = -9;
Δ = b2-4ac
Δ = 82-4·20·(-9)
Δ = 784
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{784}=28$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-28}{2*20}=\frac{-36}{40} =-9/10 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+28}{2*20}=\frac{20}{40} =1/2 $
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