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(3x-40)(2x-10)=180
We move all terms to the left:
(3x-40)(2x-10)-(180)=0
We multiply parentheses ..
(+6x^2-30x-80x+400)-180=0
We get rid of parentheses
6x^2-30x-80x+400-180=0
We add all the numbers together, and all the variables
6x^2-110x+220=0
a = 6; b = -110; c = +220;
Δ = b2-4ac
Δ = -1102-4·6·220
Δ = 6820
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6820}=\sqrt{4*1705}=\sqrt{4}*\sqrt{1705}=2\sqrt{1705}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-2\sqrt{1705}}{2*6}=\frac{110-2\sqrt{1705}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+2\sqrt{1705}}{2*6}=\frac{110+2\sqrt{1705}}{12} $
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