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5x(x-8)-8x=-10
We move all terms to the left:
5x(x-8)-8x-(-10)=0
We add all the numbers together, and all the variables
-8x+5x(x-8)+10=0
We multiply parentheses
5x^2-8x-40x+10=0
We add all the numbers together, and all the variables
5x^2-48x+10=0
a = 5; b = -48; c = +10;
Δ = b2-4ac
Δ = -482-4·5·10
Δ = 2104
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2104}=\sqrt{4*526}=\sqrt{4}*\sqrt{526}=2\sqrt{526}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{526}}{2*5}=\frac{48-2\sqrt{526}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{526}}{2*5}=\frac{48+2\sqrt{526}}{10} $
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