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7x(x-5)=-12
We move all terms to the left:
7x(x-5)-(-12)=0
We add all the numbers together, and all the variables
7x(x-5)+12=0
We multiply parentheses
7x^2-35x+12=0
a = 7; b = -35; c = +12;
Δ = b2-4ac
Δ = -352-4·7·12
Δ = 889
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{-(-35)-\sqrt{889}}{2*7}=\frac{35-\sqrt{889}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{889}}{2*7}=\frac{35+\sqrt{889}}{14} $
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