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(10x-2)(9x+5)=180
We move all terms to the left:
(10x-2)(9x+5)-(180)=0
We multiply parentheses ..
(+90x^2+50x-18x-10)-180=0
We get rid of parentheses
90x^2+50x-18x-10-180=0
We add all the numbers together, and all the variables
90x^2+32x-190=0
a = 90; b = 32; c = -190;
Δ = b2-4ac
Δ = 322-4·90·(-190)
Δ = 69424
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{69424}=\sqrt{16*4339}=\sqrt{16}*\sqrt{4339}=4\sqrt{4339}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{4339}}{2*90}=\frac{-32-4\sqrt{4339}}{180} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{4339}}{2*90}=\frac{-32+4\sqrt{4339}}{180} $
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