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10x(x+4)=90
We move all terms to the left:
10x(x+4)-(90)=0
We multiply parentheses
10x^2+40x-90=0
a = 10; b = 40; c = -90;
Δ = b2-4ac
Δ = 402-4·10·(-90)
Δ = 5200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-20\sqrt{13}}{2*10}=\frac{-40-20\sqrt{13}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+20\sqrt{13}}{2*10}=\frac{-40+20\sqrt{13}}{20} $
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