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2x(5x-3)-3x=5
We move all terms to the left:
2x(5x-3)-3x-(5)=0
We add all the numbers together, and all the variables
-3x+2x(5x-3)-5=0
We multiply parentheses
10x^2-3x-6x-5=0
We add all the numbers together, and all the variables
10x^2-9x-5=0
a = 10; b = -9; c = -5;
Δ = b2-4ac
Δ = -92-4·10·(-5)
Δ = 281
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{-(-9)-\sqrt{281}}{2*10}=\frac{9-\sqrt{281}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{281}}{2*10}=\frac{9+\sqrt{281}}{20} $
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