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(3x-10)(5x-22)=180
We move all terms to the left:
(3x-10)(5x-22)-(180)=0
We multiply parentheses ..
(+15x^2-66x-50x+220)-180=0
We get rid of parentheses
15x^2-66x-50x+220-180=0
We add all the numbers together, and all the variables
15x^2-116x+40=0
a = 15; b = -116; c = +40;
Δ = b2-4ac
Δ = -1162-4·15·40
Δ = 11056
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11056}=\sqrt{16*691}=\sqrt{16}*\sqrt{691}=4\sqrt{691}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-4\sqrt{691}}{2*15}=\frac{116-4\sqrt{691}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+4\sqrt{691}}{2*15}=\frac{116+4\sqrt{691}}{30} $
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