(0.75y-4)(0.75y-4)+(y+3)(y+3)=125

Solution for (0.75y-4)(0.75y-4)+(y+3)(y+3)=125 equation:

(0.75y-4)(0.75y-4)+(y+3)(y+3)=125

We move all terms to the left:

(0.75y-4)(0.75y-4)+(y+3)(y+3)-(125)=0

We multiply parentheses ..

(+0y^2+0y+0y+16)+(y+3)(y+3)-125=0

We get rid of parentheses

0y^2+0y+0y+(y+3)(y+3)+16-125=0

We multiply parentheses ..

0y^2+(+y^2+3y+3y+9)+0y+0y+16-125=0

We add all the numbers together, and all the variables

y^2+(+y^2+3y+3y+9)+2y-109=0

We get rid of parentheses

y^2+y^2+3y+3y+2y+9-109=0

We add all the numbers together, and all the variables

2y^2+8y-100=0

a = 2; b = 8; c = -100;
Δ = b2-4ac
Δ = 82-4·2·(-100)
Δ = 864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12\sqrt{6}}{2*2}=\frac{-8-12\sqrt{6}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12\sqrt{6}}{2*2}=\frac{-8+12\sqrt{6}}{4}
$