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(2x-7)(5x+12)=0
We multiply parentheses ..
(+10x^2+24x-35x-84)=0
We get rid of parentheses
10x^2+24x-35x-84=0
We add all the numbers together, and all the variables
10x^2-11x-84=0
a = 10; b = -11; c = -84;
Δ = b2-4ac
Δ = -112-4·10·(-84)
Δ = 3481
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{3481}=59$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-59}{2*10}=\frac{-48}{20} =-2+2/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+59}{2*10}=\frac{70}{20} =3+1/2 $
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