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5x-2x(x-5)=-7+5x+11
We move all terms to the left:
5x-2x(x-5)-(-7+5x+11)=0
We add all the numbers together, and all the variables
5x-2x(x-5)-(5x+4)=0
We multiply parentheses
-2x^2+5x+10x-(5x+4)=0
We get rid of parentheses
-2x^2+5x+10x-5x-4=0
We add all the numbers together, and all the variables
-2x^2+10x-4=0
a = -2; b = 10; c = -4;
Δ = b2-4ac
Δ = 102-4·(-2)·(-4)
Δ = 68
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{17}}{2*-2}=\frac{-10-2\sqrt{17}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{17}}{2*-2}=\frac{-10+2\sqrt{17}}{-4} $
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