7x^2+10x=2x^2+155

Solution for 7x^2+10x=2x^2+155 equation:

7x^2+10x=2x^2+155

We move all terms to the left:

7x^2+10x-(2x^2+155)=0

We get rid of parentheses

7x^2-2x^2+10x-155=0

We add all the numbers together, and all the variables

5x^2+10x-155=0

a = 5; b = 10; c = -155;
Δ = b2-4ac
Δ = 102-4·5·(-155)
Δ = 3200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-40\sqrt{2}}{2*5}=\frac{-10-40\sqrt{2}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+40\sqrt{2}}{2*5}=\frac{-10+40\sqrt{2}}{10}
$