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(2x+6)(4x-3)=5x+12
We move all terms to the left:
(2x+6)(4x-3)-(5x+12)=0
We get rid of parentheses
(2x+6)(4x-3)-5x-12=0
We multiply parentheses ..
(+8x^2-6x+24x-18)-5x-12=0
We get rid of parentheses
8x^2-6x+24x-5x-18-12=0
We add all the numbers together, and all the variables
8x^2+13x-30=0
a = 8; b = 13; c = -30;
Δ = b2-4ac
Δ = 132-4·8·(-30)
Δ = 1129
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{-(13)-\sqrt{1129}}{2*8}=\frac{-13-\sqrt{1129}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{1129}}{2*8}=\frac{-13+\sqrt{1129}}{16} $
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