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(5x-6)(2x+7)=0
We multiply parentheses ..
(+10x^2+35x-12x-42)=0
We get rid of parentheses
10x^2+35x-12x-42=0
We add all the numbers together, and all the variables
10x^2+23x-42=0
a = 10; b = 23; c = -42;
Δ = b2-4ac
Δ = 232-4·10·(-42)
Δ = 2209
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{2209}=47$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-47}{2*10}=\frac{-70}{20} =-3+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+47}{2*10}=\frac{24}{20} =1+1/5 $
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