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(5x+9)(8x+13)+(12x+3)(5x+9)=0
We multiply parentheses ..
(+40x^2+65x+72x+117)+(12x+3)(5x+9)=0
We get rid of parentheses
40x^2+65x+72x+(12x+3)(5x+9)+117=0
We multiply parentheses ..
40x^2+(+60x^2+108x+15x+27)+65x+72x+117=0
We add all the numbers together, and all the variables
40x^2+(+60x^2+108x+15x+27)+137x+117=0
We get rid of parentheses
40x^2+60x^2+108x+15x+137x+27+117=0
We add all the numbers together, and all the variables
100x^2+260x+144=0
a = 100; b = 260; c = +144;
Δ = b2-4ac
Δ = 2602-4·100·144
Δ = 10000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{10000}=100$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(260)-100}{2*100}=\frac{-360}{200} =-1+4/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(260)+100}{2*100}=\frac{-160}{200} =-4/5 $
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