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(3x+1)(4x-10)=0
We multiply parentheses ..
(+12x^2-30x+4x-10)=0
We get rid of parentheses
12x^2-30x+4x-10=0
We add all the numbers together, and all the variables
12x^2-26x-10=0
a = 12; b = -26; c = -10;
Δ = b2-4ac
Δ = -262-4·12·(-10)
Δ = 1156
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{1156}=34$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-34}{2*12}=\frac{-8}{24} =-1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+34}{2*12}=\frac{60}{24} =2+1/2 $
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