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2x(4x+9)-7(4x+9)=0
We multiply parentheses
8x^2+18x-28x-63=0
We add all the numbers together, and all the variables
8x^2-10x-63=0
a = 8; b = -10; c = -63;
Δ = b2-4ac
Δ = -102-4·8·(-63)
Δ = 2116
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{2116}=46$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-46}{2*8}=\frac{-36}{16} =-2+1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+46}{2*8}=\frac{56}{16} =3+1/2 $
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