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-4x(2x+5)+5x-1=-48
We move all terms to the left:
-4x(2x+5)+5x-1-(-48)=0
We add all the numbers together, and all the variables
5x-4x(2x+5)+47=0
We multiply parentheses
-8x^2+5x-20x+47=0
We add all the numbers together, and all the variables
-8x^2-15x+47=0
a = -8; b = -15; c = +47;
Δ = b2-4ac
Δ = -152-4·(-8)·47
Δ = 1729
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{1729}}{2*-8}=\frac{15-\sqrt{1729}}{-16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{1729}}{2*-8}=\frac{15+\sqrt{1729}}{-16} $
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