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(8x-3)(x-6)=0
We multiply parentheses ..
(+8x^2-48x-3x+18)=0
We get rid of parentheses
8x^2-48x-3x+18=0
We add all the numbers together, and all the variables
8x^2-51x+18=0
a = 8; b = -51; c = +18;
Δ = b2-4ac
Δ = -512-4·8·18
Δ = 2025
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{2025}=45$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-45}{2*8}=\frac{6}{16} =3/8 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+45}{2*8}=\frac{96}{16} =6 $
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