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(4x+10)(x+20)=90
We move all terms to the left:
(4x+10)(x+20)-(90)=0
We multiply parentheses ..
(+4x^2+80x+10x+200)-90=0
We get rid of parentheses
4x^2+80x+10x+200-90=0
We add all the numbers together, and all the variables
4x^2+90x+110=0
a = 4; b = 90; c = +110;
Δ = b2-4ac
Δ = 902-4·4·110
Δ = 6340
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6340}=\sqrt{4*1585}=\sqrt{4}*\sqrt{1585}=2\sqrt{1585}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{1585}}{2*4}=\frac{-90-2\sqrt{1585}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{1585}}{2*4}=\frac{-90+2\sqrt{1585}}{8} $
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