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(3x-6)(2x-7)+4(x-5)=0
We multiply parentheses
(3x-6)(2x-7)+4x-20=0
We multiply parentheses ..
(+6x^2-21x-12x+42)+4x-20=0
We get rid of parentheses
6x^2-21x-12x+4x+42-20=0
We add all the numbers together, and all the variables
6x^2-29x+22=0
a = 6; b = -29; c = +22;
Δ = b2-4ac
Δ = -292-4·6·22
Δ = 313
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{-(-29)-\sqrt{313}}{2*6}=\frac{29-\sqrt{313}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{313}}{2*6}=\frac{29+\sqrt{313}}{12} $
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