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x(x-8)=3x+7
We move all terms to the left:
x(x-8)-(3x+7)=0
We multiply parentheses
x^2-8x-(3x+7)=0
We get rid of parentheses
x^2-8x-3x-7=0
We add all the numbers together, and all the variables
x^2-11x-7=0
a = 1; b = -11; c = -7;
Δ = b2-4ac
Δ = -112-4·1·(-7)
Δ = 149
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{149}}{2*1}=\frac{11-\sqrt{149}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{149}}{2*1}=\frac{11+\sqrt{149}}{2} $
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