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(4x+2)(-3x+15)=18
We move all terms to the left:
(4x+2)(-3x+15)-(18)=0
We multiply parentheses ..
(-12x^2+60x-6x+30)-18=0
We get rid of parentheses
-12x^2+60x-6x+30-18=0
We add all the numbers together, and all the variables
-12x^2+54x+12=0
a = -12; b = 54; c = +12;
Δ = b2-4ac
Δ = 542-4·(-12)·12
Δ = 3492
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3492}=\sqrt{36*97}=\sqrt{36}*\sqrt{97}=6\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{97}}{2*-12}=\frac{-54-6\sqrt{97}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{97}}{2*-12}=\frac{-54+6\sqrt{97}}{-24} $
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