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4x(5-x)-11=18-5x
We move all terms to the left:
4x(5-x)-11-(18-5x)=0
We add all the numbers together, and all the variables
4x(-1x+5)-(-5x+18)-11=0
We multiply parentheses
-4x^2+20x-(-5x+18)-11=0
We get rid of parentheses
-4x^2+20x+5x-18-11=0
We add all the numbers together, and all the variables
-4x^2+25x-29=0
a = -4; b = 25; c = -29;
Δ = b2-4ac
Δ = 252-4·(-4)·(-29)
Δ = 161
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{-(25)-\sqrt{161}}{2*-4}=\frac{-25-\sqrt{161}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{161}}{2*-4}=\frac{-25+\sqrt{161}}{-8} $
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