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2x(x-5)=3x+4
We move all terms to the left:
2x(x-5)-(3x+4)=0
We multiply parentheses
2x^2-10x-(3x+4)=0
We get rid of parentheses
2x^2-10x-3x-4=0
We add all the numbers together, and all the variables
2x^2-13x-4=0
a = 2; b = -13; c = -4;
Δ = b2-4ac
Δ = -132-4·2·(-4)
Δ = 201
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{-(-13)-\sqrt{201}}{2*2}=\frac{13-\sqrt{201}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{201}}{2*2}=\frac{13+\sqrt{201}}{4} $
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