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(10x-5)(x+20)=180
We move all terms to the left:
(10x-5)(x+20)-(180)=0
We multiply parentheses ..
(+10x^2+200x-5x-100)-180=0
We get rid of parentheses
10x^2+200x-5x-100-180=0
We add all the numbers together, and all the variables
10x^2+195x-280=0
a = 10; b = 195; c = -280;
Δ = b2-4ac
Δ = 1952-4·10·(-280)
Δ = 49225
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{49225}=\sqrt{25*1969}=\sqrt{25}*\sqrt{1969}=5\sqrt{1969}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(195)-5\sqrt{1969}}{2*10}=\frac{-195-5\sqrt{1969}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(195)+5\sqrt{1969}}{2*10}=\frac{-195+5\sqrt{1969}}{20} $
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