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(5x-3)(4x+1)+(5x-3)(5x-3)=0
We multiply parentheses ..
(+20x^2+5x-12x-3)+(5x-3)(5x-3)=0
We get rid of parentheses
20x^2+5x-12x+(5x-3)(5x-3)-3=0
We multiply parentheses ..
20x^2+(+25x^2-15x-15x+9)+5x-12x-3=0
We add all the numbers together, and all the variables
20x^2+(+25x^2-15x-15x+9)-7x-3=0
We get rid of parentheses
20x^2+25x^2-15x-15x-7x+9-3=0
We add all the numbers together, and all the variables
45x^2-37x+6=0
a = 45; b = -37; c = +6;
Δ = b2-4ac
Δ = -372-4·45·6
Δ = 289
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{289}=17$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-17}{2*45}=\frac{20}{90} =2/9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+17}{2*45}=\frac{54}{90} =3/5 $
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