x(5x+5)=2x^2-3x+35

Solution for x(5x+5)=2x^2-3x+35 equation:

x(5x+5)=2x^2-3x+35

We move all terms to the left:

x(5x+5)-(2x^2-3x+35)=0

We multiply parentheses

5x^2+5x-(2x^2-3x+35)=0

We get rid of parentheses

5x^2-2x^2+5x+3x-35=0

We add all the numbers together, and all the variables

3x^2+8x-35=0

a = 3; b = 8; c = -35;
Δ = b2-4ac
Δ = 82-4·3·(-35)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-22}{2*3}=\frac{-30}{6}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+22}{2*3}=\frac{14}{6}
=2+1/3
$