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(3x-4)(5x-38)=180
We move all terms to the left:
(3x-4)(5x-38)-(180)=0
We multiply parentheses ..
(+15x^2-114x-20x+152)-180=0
We get rid of parentheses
15x^2-114x-20x+152-180=0
We add all the numbers together, and all the variables
15x^2-134x-28=0
a = 15; b = -134; c = -28;
Δ = b2-4ac
Δ = -1342-4·15·(-28)
Δ = 19636
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{19636}=\sqrt{4*4909}=\sqrt{4}*\sqrt{4909}=2\sqrt{4909}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-134)-2\sqrt{4909}}{2*15}=\frac{134-2\sqrt{4909}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-134)+2\sqrt{4909}}{2*15}=\frac{134+2\sqrt{4909}}{30} $
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