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(7x+4)(5x+10)=180
We move all terms to the left:
(7x+4)(5x+10)-(180)=0
We multiply parentheses ..
(+35x^2+70x+20x+40)-180=0
We get rid of parentheses
35x^2+70x+20x+40-180=0
We add all the numbers together, and all the variables
35x^2+90x-140=0
a = 35; b = 90; c = -140;
Δ = b2-4ac
Δ = 902-4·35·(-140)
Δ = 27700
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{27700}=\sqrt{100*277}=\sqrt{100}*\sqrt{277}=10\sqrt{277}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-10\sqrt{277}}{2*35}=\frac{-90-10\sqrt{277}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+10\sqrt{277}}{2*35}=\frac{-90+10\sqrt{277}}{70} $
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