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1+5x(x-3)=2x-14+3x
We move all terms to the left:
1+5x(x-3)-(2x-14+3x)=0
We add all the numbers together, and all the variables
5x(x-3)-(5x-14)+1=0
We multiply parentheses
5x^2-15x-(5x-14)+1=0
We get rid of parentheses
5x^2-15x-5x+14+1=0
We add all the numbers together, and all the variables
5x^2-20x+15=0
a = 5; b = -20; c = +15;
Δ = b2-4ac
Δ = -202-4·5·15
Δ = 100
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{100}=10$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10}{2*5}=\frac{10}{10} =1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10}{2*5}=\frac{30}{10} =3 $
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