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5x(90-x)=260
We move all terms to the left:
5x(90-x)-(260)=0
We add all the numbers together, and all the variables
5x(-1x+90)-260=0
We multiply parentheses
-5x^2+450x-260=0
a = -5; b = 450; c = -260;
Δ = b2-4ac
Δ = 4502-4·(-5)·(-260)
Δ = 197300
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{197300}=\sqrt{100*1973}=\sqrt{100}*\sqrt{1973}=10\sqrt{1973}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(450)-10\sqrt{1973}}{2*-5}=\frac{-450-10\sqrt{1973}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(450)+10\sqrt{1973}}{2*-5}=\frac{-450+10\sqrt{1973}}{-10} $
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