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(5x-6)(7x=12)
We move all terms to the left:
(5x-6)(7x-(12))=0
We multiply parentheses ..
(+35x^2-60x-42x+72)=0
We get rid of parentheses
35x^2-60x-42x+72=0
We add all the numbers together, and all the variables
35x^2-102x+72=0
a = 35; b = -102; c = +72;
Δ = b2-4ac
Δ = -1022-4·35·72
Δ = 324
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{324}=18$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-18}{2*35}=\frac{84}{70} =1+1/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+18}{2*35}=\frac{120}{70} =1+5/7 $
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