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(4x-5)(7x-4)=0
We multiply parentheses ..
(+28x^2-16x-35x+20)=0
We get rid of parentheses
28x^2-16x-35x+20=0
We add all the numbers together, and all the variables
28x^2-51x+20=0
a = 28; b = -51; c = +20;
Δ = b2-4ac
Δ = -512-4·28·20
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-19}{2*28}=\frac{32}{56} =4/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+19}{2*28}=\frac{70}{56} =1+1/4 $
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