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(15x-2)(7x-4)=90
We move all terms to the left:
(15x-2)(7x-4)-(90)=0
We multiply parentheses ..
(+105x^2-60x-14x+8)-90=0
We get rid of parentheses
105x^2-60x-14x+8-90=0
We add all the numbers together, and all the variables
105x^2-74x-82=0
a = 105; b = -74; c = -82;
Δ = b2-4ac
Δ = -742-4·105·(-82)
Δ = 39916
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{39916}=\sqrt{4*9979}=\sqrt{4}*\sqrt{9979}=2\sqrt{9979}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-2\sqrt{9979}}{2*105}=\frac{74-2\sqrt{9979}}{210} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+2\sqrt{9979}}{2*105}=\frac{74+2\sqrt{9979}}{210} $
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