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2x-5x(x-5)=-2+4x+13
We move all terms to the left:
2x-5x(x-5)-(-2+4x+13)=0
We add all the numbers together, and all the variables
2x-5x(x-5)-(4x+11)=0
We multiply parentheses
-5x^2+2x+25x-(4x+11)=0
We get rid of parentheses
-5x^2+2x+25x-4x-11=0
We add all the numbers together, and all the variables
-5x^2+23x-11=0
a = -5; b = 23; c = -11;
Δ = b2-4ac
Δ = 232-4·(-5)·(-11)
Δ = 309
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{-(23)-\sqrt{309}}{2*-5}=\frac{-23-\sqrt{309}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{309}}{2*-5}=\frac{-23+\sqrt{309}}{-10} $
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