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5x(x-2)=8+5x
We move all terms to the left:
5x(x-2)-(8+5x)=0
We add all the numbers together, and all the variables
5x(x-2)-(5x+8)=0
We multiply parentheses
5x^2-10x-(5x+8)=0
We get rid of parentheses
5x^2-10x-5x-8=0
We add all the numbers together, and all the variables
5x^2-15x-8=0
a = 5; b = -15; c = -8;
Δ = b2-4ac
Δ = -152-4·5·(-8)
Δ = 385
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{385}}{2*5}=\frac{15-\sqrt{385}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{385}}{2*5}=\frac{15+\sqrt{385}}{10} $
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