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(5x+1)(x-1)-24-24x=0
We add all the numbers together, and all the variables
-24x+(5x+1)(x-1)-24=0
We multiply parentheses ..
(+5x^2-5x+x-1)-24x-24=0
We get rid of parentheses
5x^2-5x+x-24x-1-24=0
We add all the numbers together, and all the variables
5x^2-28x-25=0
a = 5; b = -28; c = -25;
Δ = b2-4ac
Δ = -282-4·5·(-25)
Δ = 1284
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{321}}{2*5}=\frac{28-2\sqrt{321}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{321}}{2*5}=\frac{28+2\sqrt{321}}{10} $
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