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8x(x-1)=3x+7
We move all terms to the left:
8x(x-1)-(3x+7)=0
We multiply parentheses
8x^2-8x-(3x+7)=0
We get rid of parentheses
8x^2-8x-3x-7=0
We add all the numbers together, and all the variables
8x^2-11x-7=0
a = 8; b = -11; c = -7;
Δ = b2-4ac
Δ = -112-4·8·(-7)
Δ = 345
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{-(-11)-\sqrt{345}}{2*8}=\frac{11-\sqrt{345}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{345}}{2*8}=\frac{11+\sqrt{345}}{16} $
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