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(2x+3)(6x-5)=
We move all terms to the left:
(2x+3)(6x-5)-()=0
We add all the numbers together, and all the variables
(2x+3)(6x-5)=0
We multiply parentheses ..
(+12x^2-10x+18x-15)=0
We get rid of parentheses
12x^2-10x+18x-15=0
We add all the numbers together, and all the variables
12x^2+8x-15=0
a = 12; b = 8; c = -15;
Δ = b2-4ac
Δ = 82-4·12·(-15)
Δ = 784
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{784}=28$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-28}{2*12}=\frac{-36}{24} =-1+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+28}{2*12}=\frac{20}{24} =5/6 $
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