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(4x+1)(3x-7)-2(6x+5)=0
We multiply parentheses
(4x+1)(3x-7)-12x-10=0
We multiply parentheses ..
(+12x^2-28x+3x-7)-12x-10=0
We get rid of parentheses
12x^2-28x+3x-12x-7-10=0
We add all the numbers together, and all the variables
12x^2-37x-17=0
a = 12; b = -37; c = -17;
Δ = b2-4ac
Δ = -372-4·12·(-17)
Δ = 2185
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{-(-37)-\sqrt{2185}}{2*12}=\frac{37-\sqrt{2185}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{2185}}{2*12}=\frac{37+\sqrt{2185}}{24} $
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