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(X-10)(4X+20)=180
We move all terms to the left:
(X-10)(4X+20)-(180)=0
We multiply parentheses ..
(+4X^2+20X-40X-200)-180=0
We get rid of parentheses
4X^2+20X-40X-200-180=0
We add all the numbers together, and all the variables
4X^2-20X-380=0
a = 4; b = -20; c = -380;
Δ = b2-4ac
Δ = -202-4·4·(-380)
Δ = 6480
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-36\sqrt{5}}{2*4}=\frac{20-36\sqrt{5}}{8} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+36\sqrt{5}}{2*4}=\frac{20+36\sqrt{5}}{8} $
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