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(5d-7)(5d-6)=25d+d+42
We move all terms to the left:
(5d-7)(5d-6)-(25d+d+42)=0
We add all the numbers together, and all the variables
(5d-7)(5d-6)-(26d+42)=0
We get rid of parentheses
(5d-7)(5d-6)-26d-42=0
We multiply parentheses ..
(+25d^2-30d-35d+42)-26d-42=0
We get rid of parentheses
25d^2-30d-35d-26d+42-42=0
We add all the numbers together, and all the variables
25d^2-91d=0
a = 25; b = -91; c = 0;
Δ = b2-4ac
Δ = -912-4·25·0
Δ = 8281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{8281}=91$$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-91)-91}{2*25}=\frac{0}{50} =0 $$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-91)+91}{2*25}=\frac{182}{50} =3+16/25 $
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