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4x(x-5)-7=13-x
We move all terms to the left:
4x(x-5)-7-(13-x)=0
We add all the numbers together, and all the variables
4x(x-5)-(-1x+13)-7=0
We multiply parentheses
4x^2-20x-(-1x+13)-7=0
We get rid of parentheses
4x^2-20x+1x-13-7=0
We add all the numbers together, and all the variables
4x^2-19x-20=0
a = 4; b = -19; c = -20;
Δ = b2-4ac
Δ = -192-4·4·(-20)
Δ = 681
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{-(-19)-\sqrt{681}}{2*4}=\frac{19-\sqrt{681}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{681}}{2*4}=\frac{19+\sqrt{681}}{8} $
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