$5a+b=6a+2d=134$  

$6a+2d=134$  

$3a+d=67$  

$d=67-3a$  

$\text{Z tw. Pitagorasa:}$  

 

${\left(2a\right)}^2={30}^2+d^2$   

$4a^2=900+d^2=900+{\left(67-3a\right)}^2$   $<br>$

$900=4a^2-{\left(67-3a\right)}^2=-4489+402a-9a^2+4a^2$    

$-5a^2+402a-5389=0$  

 

$\Delta =161604-20\cdot 5389=53824$   

$\sqrt{\Delta }=232$  

 

$a_1=\frac{-402-232}{-10}=\frac{317}{5}$   

$a_2=\frac{-402+232}{-10}=17$  

 

$d_1=67-3a_1=\frac{951}{5}$  

$d_2=67-3\cdot 17=16$  

 

$134=6a+2d$  

$6a_1+2d_1\ne 134$  

$6a_2+2d_2=6\cdot 17+2\cdot 16=134$  

 

$\underline{a=17}$  

$\underline{b=17+2\cdot 16=49}$  

$\underline{2a=34}$