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3-5x(4-7x)-(3x+x)=38
We move all terms to the left:
3-5x(4-7x)-(3x+x)-(38)=0
We add all the numbers together, and all the variables
-5x(-7x+4)-(+4x)+3-38=0
We add all the numbers together, and all the variables
-5x(-7x+4)-(+4x)-35=0
We multiply parentheses
35x^2-20x-(+4x)-35=0
We get rid of parentheses
35x^2-20x-4x-35=0
We add all the numbers together, and all the variables
35x^2-24x-35=0
a = 35; b = -24; c = -35;
Δ = b2-4ac
Δ = -242-4·35·(-35)
Δ = 5476
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{5476}=74$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-74}{2*35}=\frac{-50}{70} =-5/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+74}{2*35}=\frac{98}{70} =1+2/5 $
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