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10(x-7)(4x+1)=0
We multiply parentheses ..
10(+4x^2+x-28x-7)=0
We multiply parentheses
40x^2+10x-280x-70=0
We add all the numbers together, and all the variables
40x^2-270x-70=0
a = 40; b = -270; c = -70;
Δ = b2-4ac
Δ = -2702-4·40·(-70)
Δ = 84100
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{84100}=290$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-290}{2*40}=\frac{-20}{80} =-1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+290}{2*40}=\frac{560}{80} =7 $
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