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4x^2-40x=-75
We move all terms to the left:
4x^2-40x-(-75)=0
We add all the numbers together, and all the variables
4x^2-40x+75=0
a = 4; b = -40; c = +75;
Δ = b2-4ac
Δ = -402-4·4·75
Δ = 400
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{400}=20$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-20}{2*4}=\frac{20}{8} =2+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+20}{2*4}=\frac{60}{8} =7+1/2 $
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