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(10+15x)(17x-2)=90
We move all terms to the left:
(10+15x)(17x-2)-(90)=0
We add all the numbers together, and all the variables
(15x+10)(17x-2)-90=0
We multiply parentheses ..
(+255x^2-30x+170x-20)-90=0
We get rid of parentheses
255x^2-30x+170x-20-90=0
We add all the numbers together, and all the variables
255x^2+140x-110=0
a = 255; b = 140; c = -110;
Δ = b2-4ac
Δ = 1402-4·255·(-110)
Δ = 131800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{131800}=\sqrt{100*1318}=\sqrt{100}*\sqrt{1318}=10\sqrt{1318}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-10\sqrt{1318}}{2*255}=\frac{-140-10\sqrt{1318}}{510} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+10\sqrt{1318}}{2*255}=\frac{-140+10\sqrt{1318}}{510} $
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