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13+6x(3x-7)=4+5x*3
We move all terms to the left:
13+6x(3x-7)-(4+5x*3)=0
We add all the numbers together, and all the variables
6x(3x-7)-(5x*3+4)+13=0
We multiply parentheses
18x^2-42x-(5x*3+4)+13=0
We get rid of parentheses
18x^2-42x-5x*3-4+13=0
We add all the numbers together, and all the variables
18x^2-42x-5x*3+9=0
Wy multiply elements
18x^2-42x-15x+9=0
We add all the numbers together, and all the variables
18x^2-57x+9=0
a = 18; b = -57; c = +9;
Δ = b2-4ac
Δ = -572-4·18·9
Δ = 2601
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{2601}=51$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-51}{2*18}=\frac{6}{36} =1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+51}{2*18}=\frac{108}{36} =3 $
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